Transformations 5-6 Learn to transform plane figures using translations, rotations, and reflections.

Transformations5-6

Learn to transform plane figures using translations, rotations, and reflections.

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Vocabulary

transformation

image

translation

reflection

rotation

center of rotation

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*A transformation is a change in a figure’s position or size.

Types of transformations: translation, rotation, and reflections

The resulting figure, or image, of a translation, rotation, or reflection is congruent to the original figure.

A translation slides a figure along a line without turning.

Transformations5-6

Transformations5-6

Additional Example 1: Graphing Translations on a Coordinate Plane

Graph the translation of triangle ABC 2 units right and 3 units down.

Add 2 to the x-coordinate of each vertex, and subtract 3 from the y-coordinate of each vertex.

Rule Image

A(–3, 4)A’ (–3 + 2, 4 – 3) A’(–1, 1)

B(0, 2)B’ (0 + 2, 2 – 3) B’(2, –1)

C(–2, 1)C’ (–2 + 2, 1 – 3) C’(0, –2)

A’

B’C’

Transformations5-6Check It Out: Example 1

Graph the translation of the quadrilateral ABCD 3 units down and 5 units left.

Subtract 5 from the x-coordinate of each vertex, and subtract 3 from the y-coordinate of each vertex.

Rule Image

A(1, 4)A’ (1 – 5, 4 – 3) A’(–4, 1)

B(4, 3)B’ (4 – 5, 3 – 3) B’(–1, 0)

C(4, –1)C’ (4 – 5, –1 – 3) C’(–1, –4)

C(1, –2)D’ (1 – 5, –2 – 3) D’(–4, –5)

B’A’

C’D’

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A reflection flips a figure across a line to create a mirror image.

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Transformations5-6Additional Example 2: Graphing Reflections on a

Coordinate Plane

Graph the reflection of quadrilateral ABCD across the y-axis.

Multiply the x-coordinate of each vertex by –1.

Rule Image

A(–4, 1)A’ (–1 –4, 1) A’(4, 1)

B(–2, 1)B’ (–1 –2, 1) B’(2, 1)

C(–1, –2)C’ (–1 –1, –2) C’(1, –2)

D(–4, –3)D’ (–1 –4, –3) D’(4, –3)

A’B’

C’D’

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Check It Out: Example 2

Graph the reflection of triangle FGH across the x-axis.

Multiply the y-coordinate of each vertex by –1.

Rule Image

F(–4, –2)F’ (–4, –2 –1) F’(–4, 2)

G(1, –3) G’ (1, –3 –1) G’(1, 3)

H(–2, –4)H’ (–2, –4 –1) H’(–2, 4)

H’

G’

F’

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A rotation turns a figure around a point, called the center of rotation.

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Transformations5-6Additional Example 3: Graphing Rotations on a

Coordinate Plane

Graph the rotation of triangle ABC 90 counterclockwise about the origin.

Multiply the y-coordinate of each vertex by –1, and switch the x and y coordinates.

Rule Image

A(4, 4)A’ (–1 4, 4 ) A’(–4, 4)

B(4, 1)B’ (–1 1, 4) B’(–1, 4)

C(2, 1)C’ (–1 1, 2) C’(–1, 2)

A’ B’

C’

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Check It Out: Example 3

Graph the rotation of triangle XYZ 180 about the origin.

Multiply the both coordinates by –1.

Rule Image

X(–1, 2)X’ (–1 –1, –1 2 ) X’(1, –2)

Y(2, 3)Y’ (–1 2, –1 3) Y’(–2, –3)

Z(3, 0)Z’ (–1 3, –1 0) Z’(–3, 0)

Z’

Y’X’

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Lesson QuizGraph each transformation of triangle ABC.

1. translation 4 units down

2. reflection across the y-axis

3. rotation of 180 about the origin