ABC is reflected across the y-axis. Then its image is rotated 90 about the origin. What

Vocabulary Explain the steps you would use to draw a glide reflection.

Draw the result of each composition of isometries. Translate
DEF along u and then reflect it across line
.

Draw the result of each composition of isometries. Reflect rectangle PQRS across line m and then translate it along v .

Draw the result of each composition of isometries.
ABC has vertices A (1, -1) , B (4, -1) , and C (3, 2) . Reflect
ABC across the y-axis and then translate it along the vector 0, -2.

Sports To create the opening graphics for a televised football game, an animator reflects a picture of a football helmet across line
. She then reflects its image across line m, which intersects line
at a 50 angle. Describe a single transformation that moves the helmet from its starting position to its final position.

Copy each figure and draw two lines of reflection that produce an equivalent transformation. translation:
EFG
E'F'G'

Copy each figure and draw two lines of reflection that produce an equivalent transformation. rotation with center P:
ABC
A'B'C'

Draw the result of each composition of isometries. Translate
RST along u and then translate it along v .

Draw the result of each composition of isometries. Rotate
ABC 90 about point P and then reflect it across line
.

Draw the result of each composition of isometries.
GHJ has vertices G (1, -1) , H (3, 1) , and J (3, -2) . Reflect
GHJ across the line y = x and then reflect it across the x-axis.

Games In chess, a knight moves in the shape of the letter L. The piece moves two spaces horizontally or vertically. Then it turns 90 in either direction and moves one more space. a. Describe a knights move as a composition of transformations. b. Copy the chessboard with the knight. Label all the positions the knight can reach in one move. c. Label all the positions the knight can reach in two moves.

Copy each figure and draw two lines of reflection that produce an equivalent transformation. translation: ABCD A'B'C'D'

Copy each figure and draw two lines of reflection that produce an equivalent transformation. rotation with center Q: JKL J'K'L'

////ERROR ANALYSIS///// The segment with endpoints A (4, 2) and B (2, 1) is reflected across the y-axis. The image is reflected across the x-axis. What transformation is equivalent to the composition of these two reflections? Which solution is incorrect? Explain the error.

Equilateral ABC is reflected across AB . Then its image is translated along BC . Copy ABC and draw its final image.

Tell whether each statement is sometimes, always, or never true. The composition of two reflections is equivalent to a rotation.

Tell whether each statement is sometimes, always, or never true. An isometry changes the size of a figure.

Tell whether each statement is sometimes, always, or never true. The composition of two isometries is an isometry.

Tell whether each statement is sometimes, always, or never true. A rotation is equivalent to a composition of two reflections.

Critical Thinking Given a composition of reflections across two parallel lines, does the order of the reflections matter? For example, does reflecting ABC across m and then its image across n give the same result as reflecting ABC across n and then its image across m? Explain.

Write About It Under a glide reflection, RST R'S'T '. The vertices of RST are R (-3, -2) , S (-1, -2) , and T (-1, 0) . The vertices of R'S'T ' are R'(2, 2) , S'(4, 2) , and T '(4, 0) . Describe the reflection and translation that make up the glide reflection. ge07

This problem will prepare you for the Concept Connection on page 854. The figure shows one hole of a miniature golf course where T is the tee and H is the hole. a. Yuriko makes a hole in one as shown by the red arrows. Write the balls path as a composition of translations. b. Find a different way to make a hole in one, and write the balls path as a composition of translations.

ABC is reflected across the y-axis. Then its image is rotated 90 about the origin. What are the coordinates of the final image of point A under this composition of transformations? (-1, -2) (-2, 1) (1, 2) (-2, -1)

Which composition of transformations maps
ABC into the fourth quadrant? Reflect across the x-axis and then reflect across the y-axis. Rotate about the origin by 180 and then reflect across the y-axis. Translate along the vector -5, 0 and then rotate about the origin by 90. Rotate about the origin by 90 and then translate along the vector 1, -2.

Which is equivalent to the composition of two translations? Reflection Rotation Translation Glide reflection

The point A (3, 1) is rotated 90 about the point P (-1, 2) and then reflected across the line y = 5. Find the coordinates of the image A'.

For any two congruent figures in a plane, one can be transformed to the other by a composition of no more than three reflections. Copy the figure. Show how to find a composition of three reflections that maps
MNP to
M'N'P'.

A figure in the coordinate plane is reflected across the line y = x + 1 and then across the line y = x + 3. Find a translation vector that is equivalent to the composition of the reflections. Write the vector in component form.

Determine whether the set of ordered pairs represents a function. (Previous course) (-6, -5) , (-1, 0) , (0, -5) , (1, 0)

Determine whether the set of ordered pairs represents a function. (Previous course) (-3, -1) , (1, 2) , (-3, 1) , (5, 10)

Find the length of each segment. (Lesson 11-6) EJ

Find the length of each segment. (Lesson 11-6) CD

Find the length of each segment. (Lesson 11-6) FH

Determine the coordinates of each point after a rotation about the origin by the given angle of rotation. (Lesson 12-3) F (2, 3) ; 90

Determine the coordinates of each point after a rotation about the origin by the given angle of rotation. (Lesson 12-3) N (-1, -3) ; 180

Determine the coordinates of each point after a rotation about the origin by the given angle of rotation. (Lesson 12-3) Q (-2, 0) ; 90