CK-12 Geometry - Second Edition

http://www.ck12.org Chapter 12. Rigid Transformations

(x,y)→(y,−x)

A(− 4 , 5 )→A′( 5 , 4 )

B( 1 , 2 )→B′( 2 ,− 1 )

C(− 6 ,− 2 )→C′(− 2 , 6 )

D(− 8 , 3 )→D′( 3 , 8 )

While we can rotate any image any amount of degrees, only 90◦, 180 ◦and 270◦have special rules. To rotate a figure
by an angle measure other than these three, you must use Investigation 12-1.

Example 4:Algebra ConnectionThe rotation of a quadrilateral is shown below. What is the measure ofxandy?

Solution:Because a rotation is an isometry, we can set up two equations to solve forxandy.

2 y= 80 ◦ 2 x− 3 = 15

y= 40 ◦ 2 x= 18

x= 9

Know What? RevisitedThe center of rotation is shown in the picture below. If we draw rays to the same point in
each arrow, we see that the two images are a 120◦rotation in either direction.

Review Questions

In the questions below, every rotation iscounterclockwise,unless otherwise stated.

Using Investigation 12-1, rotate each figure around pointPthe given angle measure.