Rotations & Compositions

The student is able to (I can):

• Identify and draw rotations

• Identify and draw compositions of transformations

rotation rotation rotation rotation – a transformation that turns a figure around a fixed

point, called the center of rotation.

•

center of

rotation

In the coordinate plane, we will look at two specific types of

rotations:

90° about the origin

180° about the origin

x

y

•

P(x, y)

P´(–y, x)•

90909090°°°°

•P´(–x, –y)

180180180180°°°°

( , ) ( , )x y y x→ −

( , ) ( , )x y x y→ − −

Examples

1. Rotate ΔRUG with vertices R(2, -1), U(4, 1), and G(3, 3) by

90° about the origin.

90°:

2. Rotate ΔTRI with vertices T(2, 2), R(4, -5), and I(-1, 6) by

180° about the origin.

180°:

( , ) ( , )x y y x→ −

( , ) ( , )x y x y→ − −

Examples

1. Rotate ΔRUG with vertices R(2, -1), U(4, 1), and G(3, 3) by

90° about the origin.

90°:

RRRR´́́́(1, 2), (1, 2), (1, 2), (1, 2), UUUU´́́́((((----1, 4), 1, 4), 1, 4), 1, 4), GGGG´́́́((((----3, 3)3, 3)3, 3)3, 3)

2. Rotate ΔTRI with vertices T(2, 2), R(4, -5), and I(-1, 6) by

180° about the origin.

180°:

TTTT´́́́((((----2, 2, 2, 2, ----2), 2), 2), 2), RRRR´́́́((((----4, 5), 4, 5), 4, 5), 4, 5), IIII´́́́(1, (1, (1, (1, ----6)6)6)6)

( , ) ( , )x y y x→ −

( , ) ( , )x y x y→ − −

When performing a rotation that is notnotnotnot based on multiples of

90°, you will need to use a protractor to measure the angles,

and then draw the image.

Example: Rotate the figure 60° about P.

•P

Example: Rotate the figure 60° about P.

Step 1: Draw a line from P to a vertex.

•P

Example: Rotate the figure 60° about P.

Step 1: Draw a line from P to a vertex.

Step 2: Use protractor to measure a 60° angle. You can use a

ruler or a compass to set the length.

•P

Example: Rotate the figure 60° about P.

Step 1: Draw a line from P to a vertex.

Step 2: Use protractor to measure a 60° angle. You can use a

ruler or a compass to set the length.

Step 3: Repeat for the other vertices.

•P

composition of composition of composition of composition of transformations transformations transformations transformations – performing two or more

transformations sequentially (one after another) to a

figure.

An example of a composition is a glide glide glide glide

reflectionreflectionreflectionreflection: we reflect the figure and then

translate it along a vector.