Rotations

The student is able to (I can):

Identify and draw rotations

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 RUG with vertices R(2, -1), U(4, 1), and G(3, 3) by 90 about the origin.

90:

RRRR(1, 2), U(1, 2), U(1, 2), U(1, 2), U((((----1, 4), G1, 4), G1, 4), G1, 4), G((((----3, 3)3, 3)3, 3)3, 3)

2. Rotate TRI with vertices T(2, 2), R(4, -5), and I(-1, 6) by 180 about the origin.

180:

TTTT((((----2, 2, 2, 2, ----2), R2), R2), R2), R((((----4, 5), I4, 5), I4, 5), I4, 5), I(1, (1, (1, (1, ----6)6)6)6)

(x, y) ( y, x)

(x, y) ( x, y)

When performing a rotation that is notnotnotnotbased 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 60angle. 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 60angle. You can use a ruler or a compass to set the length.

Step 3: Repeat for the other vertices.

P