12.5. Reflections http://www.ck12.org
- Reflection overx=a: If(x,y)is reflected over the vertical linex=a, then the image is( 2 a−x,y).
- Reflection overy=b: If(x,y)is reflected over the horizontal liney=b, then the image is(x, 2 b−y).
- Reflection overy=x:If(x,y)is reflected over the liney=x, then the image is(y,x).
- Reflection overy=−x:If(x,y)is reflected over the liney=−x, then the image is(−y,−x).
Example A
Reflect the letterFover thex−axis.
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.
Example B
Reflect 4 ABCover they−axis. Find the coordinates of the image.
To reflect 4 ABCover they−axis they−coordinates will remain the same. Thex−coordinates will be the same
distance away from they−axis, but on the other side of they−axis.
A( 4 , 3 )→A′(− 4 , 3 )
B( 7 ,− 1 )→B′(− 7 ,− 1 )
C( 2 ,− 2 )→C′(− 2 ,− 2 )
Example C
Reflect the triangle 4 ABCwith verticesA( 4 , 5 ),B( 7 , 1 )andC( 9 , 6 )over the linex=5.
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 D
Reflect squareABCDover the liney=x.
The purple line isy=x. To reflect an image over a line that is not vertical or horizontal, you can fold the graph on
the line of reflection.
A(− 1 , 5 )→A′( 5 ,− 1 )
B( 0 , 2 )→B′( 2 , 0 )
C(− 3 , 1 )→C′( 1 ,− 3 )
D(− 4 , 4 )→D′( 4 ,− 4 )
Watch this video for help with the Examples above.