 9.9.7.1: VOCABULARY What is a scalar?
 9.9.2.1: VOCABULARY Copy and complete: To find the sum of two matrices, add ...
 9.1: Copy and complete: A(n) ? is a transformation that preserves lengths.
 9.9.3.1: VOCABULARY What is a line of reflection?
 9.9.4.1: VOCABULARY What is a center of rotation?
 9.9.5.1: VOCABULARY Copy and complete: In a glide reflection, the direction ...
 9.9.6.1: VOCABULARY What is a center of symmetry?
 9.9.1.1: VOCABULARY Copy and complete: A ? is a quantity that has both ? and...
 9.9.7.2: WRITING If you know the scale factor, explain how to determine if a...
 9.9.2.2: WRITING How can you determine whether two matrices can be added? Ho...
 9.2: Draw a figure with exactly one line of symmetry.
 9.9.3.2: WRITING Explain how to find the distance from a point to its image ...
 9.9.4.2: WRITING Compare the coordinate rules and the rotation matrices for ...
 9.9.5.2: WRITING Explain why a glide reflection is an isometry.
 9.9.6.2: WRITING Draw a figure that has one line of symmetry and does not ha...
 9.9.1.2: WRITING Describe the difference between a vector and a ray
 9.9.7.3: IDENTIFYING DILATIONS Find the scale factor. Tell whether the dilat...
 9.9.2.3: USING A DIAGRAM Use the diagram to write a matrix to represent the ...
 9.3: WRITING Explain how to identify the dimensions of a matrix. Include...
 9.9.3.3: REFLECTIONS Graph the reflection of the polygon in the given line. ...
 9.9.4.3: IDENTIFYING TRANSFORMATIONS Identify the type of transformation, tr...
 9.9.5.3: GLIDE REFLECTION The endpoints of}CD are C(2, 25) and D(4, 0). Grap...
 9.9.6.3: LINE SYMMETRY How many lines of symmetry does the triangle have?
 9.9.1.3: IMAGE AND PREIMAGE Use the translation (x, y) (x 2 8, y 1 4). What ...
 9.9.7.4: IDENTIFYING DILATIONS Find the scale factor. Tell whether the dilat...
 9.9.2.4: USING A DIAGRAM Use the diagram to write a matrix to represent the ...
 9.4: Match the point with the appropriate name on the vector. T HT A. In...
 9.9.3.4: REFLECTIONS Graph the reflection of the polygon in the given line. ...
 9.9.4.4: IDENTIFYING TRANSFORMATIONS Identify the type of transformation, tr...
 9.9.5.4: GLIDE REFLECTION The endpoints of}CD are C(2, 25) and D(4, 0). Grap...
 9.9.6.4: LINE SYMMETRY How many lines of symmetry does the triangle have?
 9.9.1.4: IMAGE AND PREIMAGE Use the translation (x, y) (x 2 8, y 1 4). What ...
 9.9.7.5: IDENTIFYING DILATIONS Find the scale factor. Tell whether the dilat...
 9.9.2.5: USING A DIAGRAM Use the diagram to write a matrix to represent the ...
 9.5: Match the point with the appropriate name on the vector. H HT A. In...
 9.9.3.5: REFLECTIONS Graph the reflection of the polygon in the given line. ...
 9.9.4.5: IDENTIFYING TRANSFORMATIONS Identify the type of transformation, tr...
 9.9.5.5: GLIDE REFLECTION The endpoints of}CD are C(2, 25) and D(4, 0). Grap...
 9.9.6.5: LINE SYMMETRY How many lines of symmetry does the triangle have?
 9.9.1.5: IMAGE AND PREIMAGE Use the translation (x, y) (x 2 8, y 1 4). What ...
 9.9.7.6: ERROR ANALYSIS Describe and correct the error in finding the scale ...
 9.9.2.6: USING A DIAGRAM Use the diagram to write a matrix to represent the ...
 9.6: The vertices of nABC are A(2, 3), B(1, 0), and C(22, 4). Graph the ...
 9.9.3.6: REFLECTIONS Graph the reflection of the polygon in the given line. ...
 9.9.4.6: ANGLE OF ROTATION Match the diagram with the angle of rotation. x8 ...
 9.9.5.6: GLIDE REFLECTION The endpoints of}CD are C(2, 25) and D(4, 0). Grap...
 9.9.6.6: ROTATIONAL SYMMETRY Does the figure have rotational symmetry? If so...
 9.9.1.6: IMAGE AND PREIMAGE Use the translation (x, y) (x 2 8, y 1 4). What ...
 9.9.7.7: CONSTRUCTION Copy the diagram. Then draw the given dilation. JGEFH ...
 9.9.2.7: MATRIX OPERATIONS Add or subtract. f 3 5g 1 f 9 2g
 9.7: The vertices of nDEF are D(26, 7), E(25, 5), and F(28, 4). Graph th...
 9.9.3.7: REFLECTIONS Graph the reflection of the polygon in the given line. ...
 9.9.4.7: ANGLE OF ROTATION Match the diagram with the angle of rotation. x8 ...
 9.9.5.7: GRAPHING COMPOSITIONS The vertices of nPQR are P(2, 4), Q(6, 0), an...
 9.9.6.7: ROTATIONAL SYMMETRY Does the figure have rotational symmetry? If so...
 9.9.1.7: GRAPHING AN IMAGE The vertices of nPQR are P(22, 3), Q(1, 2), and R...
 9.9.7.8: CONSTRUCTION Copy the diagram. Then draw the given dilation. JGEFH ...
 9.9.2.8: MATRIX OPERATIONS Add or subtract. F212 5 1 24G 1 F 2 23 0 8G
 9.8: Find the image matrix that represents the translation of the polygo...
 9.9.3.8: REFLECTIONS Graph the reflection of the polygon in the given line. ...
 9.9.4.8: ANGLE OF ROTATION Match the diagram with the angle of rotation. x8 ...
 9.9.5.8: GRAPHING COMPOSITIONS The vertices of nPQR are P(2, 4), Q(6, 0), an...
 9.9.6.8: ROTATIONAL SYMMETRY Does the figure have rotational symmetry? If so...
 9.9.1.8: GRAPHING AN IMAGE The vertices of nPQR are P(22, 3), Q(1, 2), and R...
 9.9.7.9: CONSTRUCTION Copy the diagram. Then draw the given dilation. JGEFH ...
 9.9.2.9: MATRIX OPERATIONS Add or subtract. F 9 822 3 0 24G 1 F 7 1 2 2325 1G
 9.9: Find the image matrix that represents the translation of the polygo...
 9.9.3.9: REFLECTIONS Graph the reflection of the polygon in the given line. ...
 9.9.4.9: ROTATING A FIGURE Trace the polygon and point P on paper. Then draw...
 9.9.5.9: GRAPHING COMPOSITIONS The vertices of nPQR are P(2, 4), Q(6, 0), an...
 9.9.6.9: ROTATIONAL SYMMETRY Does the figure have rotational symmetry? If so...
 9.9.1.9: GRAPHING AN IMAGE The vertices of nPQR are P(22, 3), Q(1, 2), and R...
 9.9.7.10: CONSTRUCTION Copy the diagram. Then draw the given dilation. JGEFH ...
 9.9.2.10: MATRIX OPERATIONS Add or subtract. f 4.6 8.1g 2 f 3.8 22.1g
 9.10: Graph the reflection of the polygon in the given line. x 5 4 y11ABC
 9.9.3.10: REFLECTIONS Graph the reflection of the polygon in the given line. ...
 9.9.4.10: ROTATING A FIGURE Trace the polygon and point P on paper. Then draw...
 9.9.5.10: GRAPHING COMPOSITIONS The vertices of nPQR are P(2, 4), Q(6, 0), an...
 9.9.6.10: SYMMETRY Determine whether the figure has line symmetry and whether...
 9.9.1.10: GRAPHING AN IMAGE The vertices of nPQR are P(22, 3), Q(1, 2), and R...
 9.9.1.11: WRITING A RULE nA9B9C9 is the image of nABC after a translation. Wr...
 9.9.7.11: CONSTRUCTION Copy the diagram. Then draw the given dilation. JGEFH ...
 9.9.2.11: MATRIX OPERATIONS Add or subtract. F25 628 9G 2 F 8 10 4 27G
 9.11: Graph the reflection of the polygon in the given line. y 5 3 y13E FH G
 9.9.3.11: REFLECTIONS Graph the reflection of the polygon in the given line. ...
 9.9.4.11: ROTATING A FIGURE Trace the polygon and point P on paper. Then draw...
 9.9.5.11: REVERSING ORDERS Graph}F0G0 after a composition of the transformati...
 9.9.6.11: SYMMETRY Determine whether the figure has line symmetry and whether...
 9.9.1.12: WRITING A RULE nA9B9C9 is the image of nABC after a translation. Wr...
 9.9.7.12: CONSTRUCTION Copy the diagram. Then draw the given dilation. JGEFH ...
 9.9.2.12: MATRIX OPERATIONS Add or subtract. F 1.2 6 5.3 1.1G 2 F 2.5 23.3 7 4G
 9.12: Graph the reflection of the polygon in the given line. y 5 x y11JKL
 9.9.3.12: MULTIPLE CHOICE What is the line of reflection for nABC and its ima...
 9.9.4.12: USING COORDINATE RULES Rotate the figure the given number of degree...
 9.9.5.12: REVERSING ORDERS Graph}F0G0 after a composition of the transformati...
 9.9.6.12: SYMMETRY Determine whether the figure has line symmetry and whether...
 9.9.1.13: ERROR ANALYSIS Describe and correct the error in graphing the trans...
 9.9.7.13: CONSTRUCTION Copy the diagram. Then draw the given dilation. JGEFH ...
 9.9.2.13: TRANSLATIONS Find the image matrix that represents the translation ...
 9.13: Find the image matrix that represents the given rotation of the pol...
 9.9.3.13: USING MATRIX MULTIPLICATION Use matrix multiplication to find the i...
 9.9.4.13: USING COORDINATE RULES Rotate the figure the given number of degree...
 9.9.5.13: DESCRIBING COMPOSITIONS Describe the composition of transformations...
 9.9.6.13: MULTIPLE CHOICE Identify the line symmetry and rotational symmetry ...
 9.9.1.14: MULTIPLE CHOICE Translate Q(0, 28) using (x, y) (x 2 3, y 1 2). A Q...
 9.9.7.14: CONSTRUCTION Copy the diagram. Then draw the given dilation. JGEFH ...
 9.9.2.14: TRANSLATIONS Find the image matrix that represents the translation ...
 9.14: Find the image matrix that represents the given rotation of the pol...
 9.9.3.14: USING MATRIX MULTIPLICATION Use matrix multiplication to find the i...
 9.9.4.14: USING COORDINATE RULES Rotate the figure the given number of degree...
 9.9.5.14: DESCRIBING COMPOSITIONS Describe the composition of transformations...
 9.9.6.14: MULTIPLE CHOICE Which statement best describes the rotational symme...
 9.9.1.15: IDENTIFYING VECTORS Name the vector and write its component form. CD
 9.9.7.15: SCALAR MULTIPLICATION Simplify the product. F 3 7 4 0 9 21G
 9.9.2.15: TRANSLATIONS Find the image matrix that represents the translation ...
 9.15: Graph the image of H(24, 5) after the glide reflection. Translation...
 9.9.3.15: FINDING IMAGE MATRICES Write a matrix for the polygon. Then find th...
 9.9.4.15: USING MATRICES Find the image matrix that represents the rotation o...
 9.9.5.15: USING THEOREM 9.5 In the diagram, k i m, nABC is reflected in line ...
 9.9.6.15: ERROR ANALYSIS Describe and correct the error made in describing th...
 9.9.1.16: IDENTIFYING VECTORS Name the vector and write its component form. RT
 9.9.7.16: SCALAR MULTIPLICATION Simplify the product. 25 F22 25 7 3 1 4 0 21G
 9.9.2.16: TRANSLATIONS Find the image matrix that represents the translation ...
 9.16: Graph the image of H(24, 5) after the glide reflection. Translation...
 9.9.3.16: FINDING IMAGE MATRICES Write a matrix for the polygon. Then find th...
 9.9.4.16: USING MATRICES Find the image matrix that represents the rotation o...
 9.9.5.16: USING THEOREM 9.5 In the diagram, k i m, nABC is reflected in line ...
 9.9.6.16: ERROR ANALYSIS Describe and correct the error made in describing th...
 9.9.1.17: IDENTIFYING VECTORS Name the vector and write its component form. PJ
 9.9.7.17: SCALAR MULTIPLICATION Simplify the product. 9 F 0 3 221 7 0G
 9.9.2.17: MULTIPLE CHOICE The matrix that represents quadrilateral ABCD is F ...
 9.17: Determine whether the figure has line symmetry and/or rotational sy...
 9.9.3.17: FINDING IMAGE MATRICES Write a matrix for the polygon. Then find th...
 9.9.4.17: USING MATRICES Find the image matrix that represents the rotation o...
 9.9.5.17: USING THEOREM 9.5 In the diagram, k i m, nABC is reflected in line ...
 9.9.6.17: DRAWING FIGURES In Exercises 1720, use the description to draw a fi...
 9.9.1.18: VECTORS Use the point P(23, 6). Find the component form of the vect...
 9.9.7.18: DILATIONS WITH MATRICES Find the image matrix that represents a dil...
 9.9.2.18: MATRIX OPERATIONS Multiply. f 52gF 4 3G
 9.18: Determine whether the figure has line symmetry and/or rotational sy...
 9.9.3.18: ERROR ANALYSIS Describe and correct the error in finding the image ...
 9.9.4.18: ERROR ANALYSIS The endpoints of}AB are A(21, 1) and B(2, 3). Descri...
 9.9.5.18: USING THEOREM 9.5 In the diagram, k i m, nABC is reflected in line ...
 9.9.6.18: DRAWING FIGURES In Exercises 1720, use the description to draw a fi...
 9.9.1.19: VECTORS Use the point P(23, 6). Find the component form of the vect...
 9.9.7.19: DILATIONS WITH MATRICES Find the image matrix that represents a dil...
 9.9.2.19: MATRIX OPERATIONS Multiply. . f 1.2 3gF 2221.5G
 9.19: Determine whether the figure has line symmetry and/or rotational sy...
 9.9.3.19: MINIMUM DISTANCE Find point C on the xaxis so AC 1 BC is a minimum...
 9.9.4.19: ERROR ANALYSIS The endpoints of}AB are A(21, 1) and B(2, 3). Descri...
 9.9.5.19: USING THEOREM 9.5 In the diagram, k i m, nABC is reflected in line ...
 9.9.6.19: DRAWING FIGURES In Exercises 1720, use the description to draw a fi...
 9.9.1.20: VECTORS Use the point P(23, 6). Find the component form of the vect...
 9.9.7.20: DILATIONS WITH MATRICES Find the image matrix that represents a dil...
 9.9.2.20: MATRIX OPERATIONS Multiply. F 6 725 8GF 21 9 23G
 9.20: Find the image matrix that represents a dilation of the polygon cen...
 9.9.3.20: MINIMUM DISTANCE Find point C on the xaxis so AC 1 BC is a minimum...
 9.9.4.20: MULTIPLE CHOICE What is the value of y in the rotation of the trian...
 9.9.5.20: USING THEOREM 9.6 Find the angle of rotation that maps A onto A0. A...
 9.9.6.20: DRAWING FIGURES In Exercises 1720, use the description to draw a fi...
 9.9.1.21: VECTORS Use the point P(23, 6). Find the component form of the vect...
 9.9.7.21: COMPOSING TRANSFORMATIONS The vertices of nFGH are F(22, 22), G(22,...
 9.9.2.21: MATRIX OPERATIONS Multiply. F 0.4 626 2.3GF 5 821 2G
 9.21: Find the image matrix that represents a dilation of the polygon cen...
 9.9.3.21: MINIMUM DISTANCE Find point C on the xaxis so AC 1 BC is a minimum...
 9.9.4.21: MULTIPLE CHOICE Suppose quadrilateral QRST is rotated 1808 about th...
 9.9.5.21: USING THEOREM 9.6 Find the angle of rotation that maps A onto A0. A...
 9.9.6.21: OPENENDED MATH Draw a polygon with 1808 rotational symmetry and wi...
 9.9.1.22: TRANSLATIONS Think of each translation as a vector. Describe the ve...
 9.9.7.22: COMPOSING TRANSFORMATIONS The vertices of nFGH are F(22, 22), G(22,...
 9.9.2.22: MATRIX OPERATIONS Multiply. f 48 21gF 3 2 5G
 9.9.3.22: TWO REFLECTIONS The vertices of nFGH are F(3, 2), G(1, 5), and H(21...
 9.9.4.22: FINDING A PATTERN The vertices of nABC are A(2, 0), B(3, 4), and C(...
 9.9.5.22: ERROR ANALYSIS A student described the translation of }AB to A }9B9...
 9.9.6.22: POINT SYMMETRY In the graph, }AB is reflected in the point C to pro...
 9.9.1.23: TRANSLATIONS Think of each translation as a vector. Describe the ve...
 9.9.7.23: COMPOSING TRANSFORMATIONS The vertices of nFGH are F(22, 22), G(22,...
 9.9.2.23: MATRIX OPERATIONS Multiply. F 9 12 8 21 4GF 4 0 1G
 9.9.3.23: TWO REFLECTIONS The vertices of nFGH are F(3, 2), G(1, 5), and H(21...
 9.9.4.23: MULTIPLE CHOICE A rectangle has vertices at (4, 0), (4, 2), (7, 0),...
 9.9.5.23: USING MATRICES The vertices of nPQR are P(1, 4), Q(3, 22), and R(7,...
 9.9.6.23: SHORT RESPONSE A figure has more than one line of symmetry. Can two...
 9.9.1.24: TRANSLATING A TRIANGLE The vertices of nDEF are D(2, 5), E(6, 3), a...
 9.9.7.24: WRITING Is a composition of transformations that includes a dilatio...
 9.9.2.24: MULTIPLE CHOICE Which product is not defined? A F 17 3 12GF 6 15G B...
 9.9.3.24: TWO REFLECTIONS The vertices of nFGH are F(3, 2), G(1, 5), and H(21...
 9.9.4.24: SHORT RESPONSE Rotate the triangle in Exercise 12 908 about the ori...
 9.9.5.24: USING MATRICES The vertices of nPQR are P(1, 4), Q(3, 22), and R(7,...
 9.9.6.24: REASONING How many lines of symmetry does a circle have? How many a...
 9.9.1.25: TRANSLATING A TRIANGLE The vertices of nDEF are D(2, 5), E(6, 3), a...
 9.9.7.25: MULTIPLE CHOICE In the diagram, the center of the dilation of ~PQRS...
 9.9.2.25: OPENENDED MATH Write two matrices that have a defined product. The...
 9.9.3.25: SHORT RESPONSE Use your graphs from Exercises 2224. What do you not...
 9.9.4.25: VISUAL REASONING A point in space has three coordinates (x, y, z). ...
 9.9.5.25: OPENENDED MATH Sketch a polygon. Apply three transformations of yo...
 9.9.6.25: VISUAL REASONING How many planes of symmetry does a cube have?
 9.9.1.26: TRANSLATING A TRIANGLE The vertices of nDEF are D(2, 5), E(6, 3), a...
 9.9.7.26: REASONING The distance from the center of dilation to the image of ...
 9.9.2.26: ERROR ANALYSIS Describe and correct the error in the computation. F...
 9.9.3.26: CONSTRUCTION Use these steps to construct a reflection of nABC in l...
 9.9.4.26: CHALLENGE Rotate the line the given number of degrees (a) about the...
 9.9.5.26: CHALLENGE The vertices of nJKL are J(1, 23), K(2, 2), and L(3, 0). ...
 9.9.6.26: CHALLENGE What can you say about the rotational symmetry of a regul...
 9.9.1.27: TRANSLATING A TRIANGLE The vertices of nDEF are D(2, 5), E(6, 3), a...
 9.9.7.27: SHORT RESPONSE Graph a triangle in the coordinate plane. Rotate the...
 9.9.2.27: TRANSLATIONS Use the described translation and the graph of the ima...
 9.9.3.27: ALGEBRA The line y 5 3x 1 2 is reflected in the line y 5 21. What i...
 9.9.4.27: CHALLENGE Rotate the line the given number of degrees (a) about the...
 9.9.5.27: ANIMAL TRACKS The left and right prints in the set of animal tracks...
 9.9.6.27: WORDS Identify the line symmetry and rotational symmetry (if any) o...
 9.9.6.28: WORDS Identify the line symmetry and rotational symmetry (if any) o...
 9.9.1.28: ALGEBRA Find the value of each variable in the translation. 10sr 81...
 9.9.7.28: REASONING A dilation maps A(5, 1) to A9(2, 1) and B(7, 4) to B9(6, ...
 9.9.2.28: TRANSLATIONS Use the described translation and the graph of the ima...
 9.9.3.28: ALGEBRA Reflect the graph of the quadratic equation y 5 2x2 2 5 in ...
 9.9.4.28: CHALLENGE Rotate the line the given number of degrees (a) about the...
 9.9.5.28: ANIMAL TRACKS The left and right prints in the set of animal tracks...
 9.9.6.29: WORDS Identify the line symmetry and rotational symmetry (if any) o...
 9.9.1.29: ALGEBRA Find the value of each variable in the translation. 2055814...
 9.9.7.29: MULTIPLE CHOICE Which transformation of (x, y) is a dilation? A (3x...
 9.9.2.29: MATRIX EQUATION Use the description of a translation of a triangle ...
 9.9.3.29: REFLECTING A TRIANGLE Reflect nMNQ in the line y 5 22x. 4y 5 22xM
 9.9.4.29: ANGLE OF ROTATION Use the photo to find the angle of rotation that ...
 9.9.5.29: MULTIPLE CHOICE Which is not a glide reflection? A The teeth of a c...
 9.9.6.30: WORDS Identify the line symmetry and rotational symmetry (if any) o...
 9.9.1.30: ALGEBRA Translation A maps (x, y) to (x 1 n, y 1 m). Translation B ...
 9.9.7.30: ALGEBRA Graph parabolas of the form y 5 ax2 using three different v...
 9.9.2.30: CHALLENGE A point in space has three coordinates (x, y, z), as show...
 9.9.3.30: CHALLENGE Point B9(1, 4) is the image of B(3, 2) after a reflection...
 9.9.4.30: ANGLE OF ROTATION Use the photo to find the angle of rotation that ...
 9.9.5.30: ROWING Describe the transformations that are combined to represent ...
 9.9.6.31: KALEIDOSCOPES In Exercises 3133, use the following information abou...
 9.9.1.31: MULTISTEP PROBLEM The vertices of a rectangle are Q(2, 23), R(2, 4...
 9.9.7.31: REASONING In the graph at the right, determine whether nD9E9F9 is a...
 9.9.2.31: COMPUTERS Two computer labs submit equipment lists. A mouse costs $...
 9.9.3.31: REFLECTIONS Identify the case of the Reflection Theorem represented.
 9.9.4.31: ANGLE OF ROTATION Use the photo to find the angle of rotation that ...
 9.9.5.31: SWEATER PATTERNS In Exercises 3133, describe the transformations th...
 9.9.6.32: KALEIDOSCOPES In Exercises 3133, use the following information abou...
 9.9.1.32: CHALLENGE The vertices of nABC are A(2, 2), B(4, 2), and C(3, 4). a...
 9.9.7.32: CHALLENGE nABC has vertices A(4, 2), B(4, 6), and C(7, 2). Find the...
 9.9.2.32: SWIMMING Two swim teams submit equipment lists. The womens team nee...
 9.9.3.32: REFLECTIONS Identify the case of the Reflection Theorem represented.
 9.9.4.32: REVOLVING DOOR You enter a revolving door and rotate the door 1808....
 9.9.5.32: SWEATER PATTERNS In Exercises 3133, describe the transformations th...
 9.9.6.33: KALEIDOSCOPES In Exercises 3133, use the following information abou...
 9.9.1.33: HOME DESIGN Designers can use computers to make patterns in fabrics...
 9.9.7.33: SCIENCE You are using magnifying glasses. Use the length of the ins...
 9.9.2.33: MATRIX PROPERTIES In Exercises 3335, use matrices A, B, and C. A 5 ...
 9.9.3.33: REFLECTIONS Identify the case of the Reflection Theorem represented.
 9.9.4.33: PROVING THEOREM 9.3 Copy and complete the proof of Case 1. Case 1 T...
 9.9.5.33: SWEATER PATTERNS In Exercises 3133, describe the transformations th...
 9.9.6.34: CHEMISTRY The diagram at the right shows two forms of the amino aci...
 9.9.1.34: HOME DESIGN Designers can use computers to make patterns in fabrics...
 9.9.7.34: SCIENCE You are using magnifying glasses. Use the length of the ins...
 9.9.2.34: MATRIX PROPERTIES In Exercises 3335, use matrices A, B, and C. A 5 ...
 9.9.3.34: DELIVERING PIZZA You park at some point K on line n. You deliver a ...
 9.9.4.34: PROVING THEOREM 9.3 Write a proof for Case 2 and Case 3. (Refer to ...
 9.9.5.34: SHORT RESPONSE Use Theorem 9.5 to explain how you can make a glide ...
 9.9.6.35: MULTISTEP PROBLEM The Castillo de San Marcos in St. Augustine, Flo...
 9.9.1.35: SNOWSHOEING You are snowshoeing in the mountains. The distances in ...
 9.9.7.35: SCIENCE You are using magnifying glasses. Use the length of the ins...
 9.9.2.35: MATRIX PROPERTIES In Exercises 3335, use matrices A, B, and C. A 5 ...
 9.9.3.35: PROVING THEOREM 9.2 Prove Case 1 of the Reflection Theorem. Case 1 ...
 9.9.4.35: PROVING THEOREM 9.3 Write a proof for Case 2 and Case 3. (Refer to ...
 9.9.5.35: PROVING THEOREM 9.4 Write a plan for proof for one case of the Comp...
 9.9.6.36: CHALLENGE Spirals have a type of symmetry called spiral, or helical...
 9.9.1.36: SNOWSHOEING You are snowshoeing in the mountains. The distances in ...
 9.9.7.36: MURALS A painter sketches plans for a mural. The plans are 2 feet b...
 9.9.2.36: ART Two art classes are buying supplies. A brush is $4 and a paint ...
 9.9.3.36: PROVING THEOREM 9.2 In Exercises 3638, write a proof for the given ...
 9.9.4.36: MULTISTEP PROBLEM Use the graph of y 5 2x 2 3. a. Rotate the line ...
 9.9.5.36: PROVING THEOREM 9.4 A composition of a rotation and a reflection, a...
 9.9.6.37: Solve the proportion. (p. 356) 5}x 5 15}27
 9.9.1.37: SNOWSHOEING You are snowshoeing in the mountains. The distances in ...
 9.9.7.37: PHOTOGRAPHY By adjusting the distance between the negative and the ...
 9.9.2.37: CHALLENGE The total United States production of corn was 8,967 mill...
 9.9.3.37: PROVING THEOREM 9.2 In Exercises 3638, write a proof for the given ...
 9.9.4.37: EXTENDED RESPONSE Use the graph of the quadratic equation y 5 x2 1 ...
 9.9.5.37: PROVING THEOREM 9.5 Prove the Reflection in Parallel Lines Theorem....
 9.9.6.38: Solve the proportion. (p. 356) a}1 47 5 49}56
 9.9.1.38: HANG GLIDING A hang glider travels from point A to point D. At poin...
 9.9.7.38: OPENENDED MATH Graph a polygon in a coordinate plane. Draw a figur...
 9.9.2.38: Copy the figure and draw its image after the reflection. (p. 272) x...
 9.9.3.38: PROVING THEOREM 9.2 In Exercises 3638, write a proof for the given ...
 9.9.4.38: TWO ROTATIONS The endpoints of }FG are F(1, 2) and G(3, 4). Graph}F...
 9.9.5.38: PROVING THEOREM 9.6 Prove the Reflection in Intersecting Lines Theo...
 9.9.6.39: Solve the proportion. (p. 356) 52b 2 3 5}13b 1 1
 9.9.1.39: HANG GLIDING A hang glider travels from point A to point D. At poin...
 9.9.7.39: MULTISTEP PROBLEM Use the figure at the right. a. Write a polygon ...
 9.9.2.39: Copy the figure and draw its image after the reflection. (p. 272) x...
 9.9.3.39: REFLECTING POINTS Use C(1, 3). a. Point A has coordinates (21, 1). ...
 9.9.4.39: TWO ROTATIONS The endpoints of }FG are F(1, 2) and G(3, 4). Graph}F...
 9.9.5.39: VISUAL REASONING You are riding a bicycle along a flat street. a. W...
 9.9.6.40: Determine whether the dilation from Figure A to Figure B is a reduc...
 9.9.1.40: HANG GLIDING A hang glider travels from point A to point D. At poin...
 9.9.7.40: AREA You have an 8 inch by 10 inch photo. a. What is the area of th...
 9.9.2.40: Find the value of x to the nearest tenth. (p. 466) 31558x
 9.9.3.40: PHYSICS The Law of Reflection states that the angle of incidence is...
 9.9.4.40: CHALLENGE A polar coordinate system locates a point in a plane by i...
 9.9.5.40: MULTISTEP PROBLEM A point in space has three coordinates (x, y, z)...
 9.9.6.41: Determine whether the dilation from Figure A to Figure B is a reduc...
 9.9.1.41: HANG GLIDING A hang glider travels from point A to point D. At poin...
 9.9.7.41: REASONING You put a reduction of a page on the original page. Expla...
 9.9.2.41: Find the value of x to the nearest tenth. (p. 466) 13428x
 9.9.3.41: PHYSICS The Law of Reflection states that the angle of incidence is...
 9.9.4.41: In the diagram, ] DC is the perpendicular bisector of}AB . (p. 303)...
 9.9.5.41: CHALLENGE Justify the following conjecture or provide a counterexam...
 9.9.6.42: Write a matrix to represent the given polygon. (p. 580) Triangle A ...
 9.9.1.42: EXTENDED RESPONSE Use the equation 2x 1 y 5 4. a. Graph the line an...
 9.9.7.42: CHALLENGE Draw two concentric circles with center A. Draw }AB and }...
 9.9.2.42: Find the value of x to the nearest tenth. (p. 466) 10258
 9.9.3.42: Tell whether the lines through the given points are parallel, perpe...
 9.9.4.42: In the diagram, ] DC is the perpendicular bisector of}AB . (p. 303)...
 9.9.5.42: Find the unknown side length. Write your answer in simplest radical...
 9.9.6.43: Write a matrix to represent the given polygon. (p. 580) Triangle B ...
 9.9.1.43: SCIENCE You are studying an amoeba through a microscope. Suppose th...
 9.9.7.43: Find the unknown leg length x. (p. 433) x60 3
 9.9.2.43: The diagonals of rhombus WXYZ intersect at V. Given that m XYW 5 62...
 9.9.3.43: Tell whether the lines through the given points are parallel, perpe...
 9.9.4.43: In the diagram, ] DC is the perpendicular bisector of}AB . (p. 303)...
 9.9.5.43: Find the unknown side length. Write your answer in simplest radical...
 9.9.6.44: Write a matrix to represent the given polygon. (p. 580) Pentagon A ...
 9.9.1.44: MULTISTEP PROBLEM You can write the equation of a parabola in the ...
 9.9.7.44: Find the unknown leg length x. (p. 433) x757
 9.9.2.44: The diagonals of rhombus WXYZ intersect at V. Given that m XYW 5 62...
 9.9.3.44: Quadrilateral EFGH is a kite. Find m G. (p. 542) H FEG1058 508
 9.9.4.44: Use a sine or cosine ratio to find the value of each variable. Roun...
 9.9.5.44: Find the unknown side length. Write your answer in simplest radical...
 9.9.6.45: Write a matrix to represent the given polygon. (p. 580) Pentagon B ...
 9.9.1.45: TECHNOLOGY The standard form of an exponential equation is y 5 ax ,...
 9.9.7.45: Find the unknown leg length x. (p. 433) 125325
 9.9.2.45: The diagonals of rhombus WXYZ intersect at V. Given that m XYW 5 62...
 9.9.3.45: Quadrilateral EFGH is a kite. Find m G. (p. 542) E GFH100855
 9.9.4.45: Use a sine or cosine ratio to find the value of each variable. Roun...
 9.9.5.45: The coordinates of nPQR are P(3, 1), Q(3, 3), and R(6, 1). Graph th...
 9.9.1.46: CHALLENGE Use properties of congruent triangles to prove part of Th...
 9.9.7.46: Find the sum of the measures of the interior angles of the indicate...
 9.9.3.46: Quadrilateral EFGH is a kite. Find m G. (p. 542) HGE808
 9.9.4.46: Use a sine or cosine ratio to find the value of each variable. Roun...
 9.9.5.46: The coordinates of nPQR are P(3, 1), Q(3, 3), and R(6, 1). Graph th...
 9.9.1.47: Find the sum, difference, product, or quotient. (p. 869) 216 2 7
 9.9.7.47: Find the sum of the measures of the interior angles of the indicate...
 9.9.5.47: The coordinates of nPQR are P(3, 1), Q(3, 3), and R(6, 1). Graph th...
 9.9.1.48: Find the sum, difference, product, or quotient. (p. 869) 6 1 (212)
 9.9.7.48: Find the sum of the measures of the interior angles of the indicate...
 9.9.5.48: The coordinates of nPQR are P(3, 1), Q(3, 3), and R(6, 1). Graph th...
 9.9.1.49: Find the sum, difference, product, or quotient. (p. 869) (13)(22)
 9.9.7.49: Find the sum of the measures of the interior angles of the indicate...
 9.9.1.50: Find the sum, difference, product, or quotient. (p. 869) 16 4 (24)
 9.9.1.51: Determine whether the two triangles are similar. If they are, write...
 9.9.1.52: Determine whether the two triangles are similar. If they are, write...
 9.9.1.53: Points A, B, C, and D are the vertices of a quadrilateral. Give the...
 9.9.1.54: Points A, B, C, and D are the vertices of a quadrilateral. Give the...
Solutions for Chapter 9: Translate Figures and Use Vectors
Full solutions for Geometry (Holt McDougal Larson Geometry)  1st Edition
ISBN: 9780618595402
Solutions for Chapter 9: Translate Figures and Use Vectors
Get Full SolutionsThis textbook survival guide was created for the textbook: Geometry (Holt McDougal Larson Geometry), edition: 1. This expansive textbook survival guide covers the following chapters and their solutions. Since 354 problems in chapter 9: Translate Figures and Use Vectors have been answered, more than 26331 students have viewed full stepbystep solutions from this chapter. Geometry (Holt McDougal Larson Geometry) was written by and is associated to the ISBN: 9780618595402. Chapter 9: Translate Figures and Use Vectors includes 354 full stepbystep solutions.

Associative Law (AB)C = A(BC).
Parentheses can be removed to leave ABC.

Column space C (A) =
space of all combinations of the columns of A.

Dot product = Inner product x T y = XI Y 1 + ... + Xn Yn.
Complex dot product is x T Y . Perpendicular vectors have x T y = O. (AB)ij = (row i of A)T(column j of B).

Graph G.
Set of n nodes connected pairwise by m edges. A complete graph has all n(n  1)/2 edges between nodes. A tree has only n  1 edges and no closed loops.

Identity matrix I (or In).
Diagonal entries = 1, offdiagonal entries = 0.

Incidence matrix of a directed graph.
The m by n edgenode incidence matrix has a row for each edge (node i to node j), with entries 1 and 1 in columns i and j .

Lucas numbers
Ln = 2,J, 3, 4, ... satisfy Ln = L n l +Ln 2 = A1 +A~, with AI, A2 = (1 ± /5)/2 from the Fibonacci matrix U~]' Compare Lo = 2 with Fo = O.

Matrix multiplication AB.
The i, j entry of AB is (row i of A)·(column j of B) = L aikbkj. By columns: Column j of AB = A times column j of B. By rows: row i of A multiplies B. Columns times rows: AB = sum of (column k)(row k). All these equivalent definitions come from the rule that A B times x equals A times B x .

Multiplier eij.
The pivot row j is multiplied by eij and subtracted from row i to eliminate the i, j entry: eij = (entry to eliminate) / (jth pivot).

Outer product uv T
= column times row = rank one matrix.

Pivot.
The diagonal entry (first nonzero) at the time when a row is used in elimination.

Polar decomposition A = Q H.
Orthogonal Q times positive (semi)definite H.

Row picture of Ax = b.
Each equation gives a plane in Rn; the planes intersect at x.

Singular matrix A.
A square matrix that has no inverse: det(A) = o.

Solvable system Ax = b.
The right side b is in the column space of A.

Spanning set.
Combinations of VI, ... ,Vm fill the space. The columns of A span C (A)!

Special solutions to As = O.
One free variable is Si = 1, other free variables = o.

Tridiagonal matrix T: tij = 0 if Ii  j I > 1.
T 1 has rank 1 above and below diagonal.

Vector space V.
Set of vectors such that all combinations cv + d w remain within V. Eight required rules are given in Section 3.1 for scalars c, d and vectors v, w.

Wavelets Wjk(t).
Stretch and shift the time axis to create Wjk(t) = woo(2j t  k).