CK-12 Geometry - Second Edition

(Marvins-Underground-K-12) #1

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


Example 2:Reflect the letter “F′′over thex−axis.


Solution:To reflect the letterFover thex−axis, now thex−coordinates will remain the same and they−coordinates
will be the same distance away from thex−axis on the other side.


The generalized rule for reflecting a figure over thex−axis:


Reflection over thex−axis: If(x,y)is reflected over thex−axis, then the image is(x,−y).


Reflections over Horizontal and Vertical Lines


Other than thexandyaxes, we can reflect a figure over any vertical or horizontal line.


Example 3:Reflect the triangle 4 ABCwith verticesA( 4 , 5 ),B( 7 , 1 )andC( 9 , 6 )over the linex=5.


Solution:Notice that this vertical line is through our preimage. Therefore, the image’s vertices are the same distance
away fromx=5 as the preimage. As with reflecting over they−axis (orx=0), they−coordinates will stay the
same.


A( 4 , 5 )→A′( 6 , 5 )


B( 7 , 1 )→B′( 3 , 1 )


C( 9 , 6 )→C′( 1 , 6 )


Example 4:Reflect the line segmentPQwith endpointsP(− 1 , 5 )andQ( 7 , 8 )over the liney=5.

Free download pdf