Solution: ?Graph each figure. Then find the coordinates of the vertices after the given

Graph each equation using the slope and \(y\)-intercept. \(y=2 x-3\) Equation Transcription: Text Transcription: y y = 2x - 3

Graph each equation using the slope and \(y\)-intercept. \(y=-x+2\) Equation Transcription: Text Transcription: y y = -x + 2

Graph each equation using the slope and \(y\)-intercept. \(y=-1\) Equation Transcription: Text Transcription: y y = -1

Graph each equation using the slope and \(y\)-intercept. \(2 x+3 y=6\) Equation Transcription: Text Transcription: y 2x + 3y = 6

Graph each equation using the slope and \(y\)-intercept. \(3 x+4 y=12\) Equation Transcription: Text Transcription: y 3x + 4y = 12

Graph each equation using the slope and \(y\)-intercept. \(5 x-y=2\) Equation Transcription: Text Transcription: y 5x - y = 2

Determine whether each figure has line symmetry. If it does, copy the figure, and draw all lines of symmetry. If not, write no.

Determine whether each figure has line symmetry. If it does, copy the figure, and draw all lines of symmetry. If not, write no.

Determine whether each figure has line symmetry. If it does, copy the figure, and draw all lines of symmetry. If not, write no.

Determine whether each figure has rotational symmetry. Write yes or no.

Determine whether each figure has rotational symmetry. Write yes or no.

Determine whether each figure has rotational symmetry. Write yes or no.

Determine whether each pair of polygons is similar. Justify your answer.

Determine whether each pair of polygons is similar. Justify your answer.

Solve each system of equations by graphing. (Lesson 16–1) \(\begin{array}{l} y=\frac{1}{2} x+3 \\ x=4 \end{array} \) Equation Transcription: Text Transcription: y=1/2x+3 x=4

Solve each system of equations by graphing. (Lesson 16–1) \(\begin{array}{l} -x+y=6 \\ -3 x+3 y=3 \end{array} \) Equation Transcription: Text Transcription: -x+y=6 -3x+3y=3

Use substitution or elimination to solve each system of equations. (Lesson 16–2) \(\begin{array}{l} x=5-y \\ 3 y=3 x+1 \end{array} \) Equation Transcription: Text Transcription: x=5-y 3y=3x+1

Use substitution or elimination to solve each system of equations. (Lesson 16–2) \(\begin{array}{l} 2 x+3 y=11 \\ 4 x-7 y=35 \end{array} \) Equation Transcription: Text Transcription: 2x+3y=11 4x-7y=35

Sales Used Music sells CDs for $9 and cassette tapes for $4. Suppose x represents the number of CDs sold and y represents the number of cassette tapes sold. Then x + y = 38 describes the total number sold in one afternoon and 9x + 4y = 297 describes the total sales during that time. (Lesson 16–2) a. Solve the system of equations. b. How many more CDs than cassette tapes were sold?

Graph each figure. Then find the coordinates of the vertices after the given transformation and graph the image. Figure Vertices Transformation ?HIJ H(-2, 1), I(2, 3), J(0, 0) translated by (2, 4) (Lesson 16–3)

Graph each figure. Then find the coordinates of the vertices after the given transformation and graph the image. Figure Vertices Transformation ?EFG E(2, 0), F(-1, -1), G(1, 3) translated by (3, 1) (Lesson 16–3)

Graph each figure. Then find the coordinates of the vertices after the given transformation and graph the image. Figure Vertices Transformation ?ABC A(-4,-2), B(-1,-4), C(2, -2) reflected over x-axis (Lesson 16–4)

Graph each figure. Then find the coordinates of the vertices after the given transformation and graph the image. Figure Vertices Transformation quadrilateral QRST Q(1, 0), R(2,-3), S(0,-3), T(-3, -1) reflected over y-axis (Lesson 16–4)

Design Describe how rotation was used to create the design at the right and list the angles of rotation that were used. (Lesson 16–5)

Use a pencil, straightedge, and grid paper to explore composition of transformations. a.Draw and label the x-axis and y-axis on the grid paper. Use a straightedge to draw a triangle with vertices A(3, 1), B(5, 2), andC(4, 6). b. Draw the reflection of ?ABC over the x-axis and label it ?A’B’C. c. Draw the reflection of ?A’B’C over the y-axis and label it ?A”B”C”. Record the coordinates of the vertices of ?A”B”C” in a table d. Rotate ?ABC 180°clockwise about the origin. Record the coordinates of the vertices in a table. How do these coordinates compare to the coordinates in part c? What can you conclude?

Repeat Exercise 1, this time reflecting the triangle over the x-axis, and then over the line y = -7. Is there a way to get to this image by performing justone transformation? Explain.

Fractals Mathematician BenoitMandelbrot used the term fractal to describe things in nature that are irregular in shape, such as clouds,coastlines, and trees. Fractals are self-similar; that is, the smaller details of the shape have the same characteristics as the original form.Describe how transformations and compositions of transformations could be used to draw a picture of a fractal.

State whether each sentence is true or false. If false, replace the underlined word(s) to make a true statement. Adilation alters the size of a figure but does not change its shape.

State whether each sentence is true or false. If false, replace the underlined word(s) to make a true statement. Substitution and elimination are methods for solving translations.

State whether each sentence is true or false. If false, replace the underlined word(s) to make a true statement. A reflection is the turning of a figure about a fixed point.

State whether each sentence is true or false. If false, replace the underlined word(s) to make a true statement. A figure is reduced in a dilation if the scale factor is between 0 and 1.

State whether each sentence is true or false. If false, replace the underlined word(s) to make a true statement. In a reflection, a figure is moved from one position to another without turning.

State whether each sentence is true or false. If false, replace the underlined word(s) to make a true statement. Systems of equations can be solved algebraically by elimination.

State whether each sentence is true or false. If false, replace the underlined word(s) to make a true statement. The fixed point about which a figure is rotated is called the center of rotation.

State whether each sentence is true or false. If false, replace the underlined word(s) to make a true statement. A rotation flips a figure over a line.

State whether each sentence is true or false. If false, replace the underlined word(s) to make a true statement. It is better to use substitution to solve a system of equations when one of the equations is already solved for a variable.

State whether each sentence is true or false. If false, replace the underlined word(s) to make a true statement. Another name for a rotation is a reflection.

Solve each system of equations by graphing. x + y = 4 y = 2x + 1

Solve each system of equations by graphing. y = x - 5 y = x + 5

Solve each system of equations by graphing. 3y = 9 15 - y = 9

Solve each system of equations by graphing. y = -x + 6 -2x + y = 6

State whether substitution or elimination would be better to solve each system of equations. Explain your reasoning. Then Solve the system. 5x + 6 = 11 x - y = 7

State whether substitution or elimination would be better to solve each system of equations. Explain your reasoning. Then Solve the system. -2x + y = 40 3x + 7y = 195

State whether substitution or elimination would be better to solve each system of equations. Explain your reasoning. Then Solve the system. 7x - y = -10 2x + 2y = 52

State whether substitution or elimination would be better to solve each system of equations. Explain your reasoning. Then Solve the system. -x + 6y = 8 x - y = 2

State whether substitution or elimination would be better to solve each system of equations. Explain your reasoning. Then Solve the system. 4x + 12y = -4 -x - 5y = 3

Graph each figure. Then find the coordinates of the vertices after the given translation and graph its translationimage. quadrilateral ABCD with vertices A(1, 1),B(1, 5), C(7, 5), and D(7, 1) translated by(-2, -3)

Graph each figure. Then find the coordinates of the vertices after the given translation and graph its translationimage. triangle LMN with vertices L(-3, 1), M(0, 3), and N(1, -1) translated by (1, 1)

Graph each figure. Then find the coordinates of the vertices after a reflection over the given axis and graph the reflection image. triangle DEF with vertices D(0, 3), E(3, 3),and F(1, 1) reflected over the x-axis

Graph each figure. Then find the coordinates of the vertices after a reflection over the given axis and graph the reflection image. quadrilateral STUV with vertices S(0, 2),T(4, -1), U(2, 1), and V(-1, -2) reflected over the y-axis

Rotate quadrilateral WXYZ 45° counterclockwise about point W by tracing.

Find the coordinates of ?STR if the figure is rotated 90° clockwise about the origin. Then graph the rotation image.

Graph each figure. Then find the coordinates of the dilation image for the given scale factor k, and graph the dilation image. ?DEF with vertices D(0, 0), E(2, -4), and F(-2, -2); k = \(\frac{1}{2}\) Equation Transcription: Text Transcription: 1/2

Graph each figure. Then find the coordinates of the dilation image for the given scale factor k, and graph the dilation image. quadrilateral QRST with vertices Q(0, 1), R(0, 0), S(-1, -1), and T(-2, 1); k = 3

Graph each figure. Then find the coordinates of the dilation image for the given scale factor k, and graph the dilation image. quadrilateral ABCD with vertices A(-2, 2), B(2, 2), C(2, -1), and D(-2, -1); k = 2

Fund-raiser The Central Middle School chorale sold hot dogs for $2 and cookies for $1 to raise funds for a new piano. If x represents the number of hot dogs sold and y represents the number of cookies sold, then x + y = 220 describes the total number of items sold and 2x + y = 368 describes the money they made. How many hot dogs and cookies were sold? (Lesson 16–2)

School Spirit Gina is designing a large banner for an after-school pep rally. If the scale factor of her design to the actual banner is \(\frac{1}{8}\) and the dimensions of the design are 2 feet by 3 feet, what will be the dimensions of the completed banner? (Lesson 16–6) Equation Transcription: Text Transcription: 1/8

List the four types of transformations in this chapter and give a brief description and an example of each.

Describe Three methods for solving a system of equations.

Solve each system of equations by graphing. x + 4y = 0 y = -x - 3

Solve each system of equations by graphing. y = \(-\frac{1}{2} x-2\) x - 2y = 12 Equation Transcription: Text Transcription: -1/2 x - 2

Solve each system of equations by graphing. y = 5x + 1 x + y = 7

Solve each system of equations by substitution or elimination. \(-x+y=2\) \(3x-2y=5\) Equation Transcription: Text Transcription: -x+y=2 3x-2y=5

Solve each system of equations by substitution or elimination. \(x-4y=1\) \(3x+4y=7\) Equation Transcription: Text Transcription: x-4y=1 3x+4y=7

Solve each system of equations by substitution or elimination. \(2x+2y=-18\) \(6x-y=2\) Equation Transcription: Text Transcription: 2x+2y=-18 6x-y=2

Graph each figure. Then find the coordinates of the vertices after the given transformation and graph the image. Figure Vertices Transformation \(\triangle P Q R\) P(-2, 0), Q(0, -1), R(-3, -3) reflected over the y-axis Equation Transcription: Text Transcription: triangle PQR

Graph each figure. Then find the coordinates of the vertices after the given transformation and graph the image. Figure Vertices Transformation quadrilateral HIJK H(-2, 4), I(-1, 2), J(-2, 1), K(-4, 2) rotated \(90^{\circ}\) clockwise about the origin Equation Transcription: Text Transcription: 90 degrees

Graph each figure. Then find the coordinates of the vertices after the given transformation and graph the image. Figure Vertices Transformation \(\triangle A B C\) A(-2, 3), B(-1, 2), C(-4, 1) translated by (5, -2) Equation Transcription: Text Transcription: triangle ABC

Graph each figure. Then find the coordinates of the vertices after the given transformation and graph the image. Figure Vertices Transformation Square WXYZ W(1, 2), X(3, 2), Y(3, 0), Z(1, 0) reflected over the x-axis

Graph each figure. Then find the coordinates of the vertices after the given transformation and graph the image. Figure Vertices Transformation \(\triangle E F G\) E(-1, 0), F(0, -3), G(-3, -1) rotated \(90^{\circ}\) counterclockwise about the origin Equation Transcription: Text Transcription: triangle EFG

Find the coordinates of the dilation image for a scale factor of 2. Then graph the dilation image.

Landscaping Mr. Collins is landscaping his yard. He plans to move a storage shed from the side of his house to the corner of the yard. Suppose the vertices at the corners of the base of the shed are S(32, 35), H(42, 35), E(42, 27), and D(32, 27). If the shed is moved 15 feet across the yard and 81 feet back, the translation can be given by (15, 81). Find the coordinates of the vertices after the shed is moved.

Office Equipment Most copy machines can reduce and enlarge images. It is necessary to reduce a rectangular image from 16 cm by 20 cm to 12 cm by 15 cm. What scale factor should be used?

Rachel has $100 in her savings account and deposits an additional $25 per week. Nina has $360 in her account and is saving $5 per week. After how many weeks will the girls have the same amount? (Algebra Review) (a) 10 (b) 11 (c) 12 (d) 13

If \(\triangle W X Y\) is translated 5 units right and 3 units up to become \(\triangle W^{\prime} X^{\prime} Y^{\prime}\), where is \(Y^{\prime}\)? (a) (6, 3) (b) (7, 3) (c) (7, 4) (d) (3, 7) Equation Transcription: Text Transcription: triangle WXY triangle W'X'Y' Y'

For all \(y \neq 3, \frac{y^{2}-9}{3 y-9}=\)? (Algebra Review) (a) y (b) \(y+1\) (c) \(\frac{y}{3}\) (d) \(\frac{y+3}{3}\) Equation Transcription: Text Transcription: Transcription: y neq 3, y^2-9 / 3y-9= y+1 y/3 y+3/3

What is the mode of the ages? (Statistics Review) (a) 3 (b) 4 (c) 5 (d) 6

If \(\square A B C D\) is reflected over the y-axis to become \(\square A^{\prime} B^{\prime} C^{\prime} D^{\prime}\), what are the coordinates of \(C^{\prime}\)? (Lesson 16–4) (a) (1, -1) (b) (-1, -1) (c) (1, 1) (d) (-1, 1) Equation Transcription: ? ? Text Transcription: square ABCD square A'B'C'D' C'

\(\left(10 x^{4}-x^{2}+2 x-8\right)-\left(3 x^{4}+3 x^{3}+2 x+8\right)=\) (Algebra Review) (a) \(7 x^{4}-3 x^{3}-x^{2}-16\) (b) \(7 x^{4}-4 x^{2}-16\) (c) \(7 x^{4}+3 x^{3}-x^{2}+4 x\) (d) \(7 x^{4}+2 x^{2}+4 x\) (e) \(13 x^{4}-3 x^{3}+x^{2}+4 x\) Equation Transcription: Text Transcription: (10x^4 - x^2 + 2x-8)-(3x^4 + 3x^3 + 2x+8)= 7x^4 - 3x^3 - x^2 - 16 7x^4 - 4x^2 - 16 7x^4 + 3x^3 - x^2 + 4x 7x^4 + 2x^2 + 4x 13x^4 - 3x^3 + x^2 + 4x

A two-digit number is 7 times its unit digit. If 18 is added to the number, its digits are reversed. Find the number. (Algebra Review) (a) 24 (b) 30 (c) 32 (d) 35

What is the area of the triangle in terms of the radius \(r\) of the circle? (Lesson 14–1) (a) \(\frac{1}{2} r^{2} \text { units }^{2}\) (b) \(r^{2} \text { units }^{2}\)\) (c) \(\frac{\pi r^{2}}{2} \text { units }^{2}\) (d) \(2 r^{2} \text { units }^{2}\) Equation Transcription: Text Transcription: 1/2 r^2 units^2 r^2 units^2 pi r^2 / 2 units^2 2r^2 units^2

Grid-In The average of \(x\) and \(y\) is 100, and the ratio of \(x\) to \(y\) is 3 to 2. What is the value of \(x-y\)? (Statistics Review) Equation Transcription: Text Transcription: x y x y x-y

A student group is taking a field trip on a bus that holds at most 40 people. Student tickets cost $4, and chaperone tickets cost $7. The group has $196. (Algebra Review) Part A Write a system of two inequalities to find the number of students \(s\) and number of chaperones \(c\) that can go on the trip. Part B Graph the inequalities in the first quadrant. Label the region that is the solution. Give one example of a solution. Equation Transcription: Text Transcription: s c