8.1 Transformation – Reflections
Name ____________________ Per. ____
Defining Characteristics:
 Corresponding points are the same distance from the line of reflection.
 A straight line drawn between corresponding points is perpendicular (opposite sign and
inverse) to the line of reflection.
1. Determine the coordinates of
EFG
E __________ F ____________ G ___________
2. Determine the coordinates of E’F’G’ if
is
reflected over the x-axis. Graph & label the new triangle.
E’ __________ F’ ____________ G’ ___________
3. Determine the coordinates of
E’’F’’G’’ if
is
reflected over the y-axis. Graph & label the new triangle.
E’’ ___________ F’’ ____________ G’’ ____________
Reflecting a figure over the x-axis changes its ______ value. (x,y)
Reflecting a figure over the y-axis changes its ______ value. (x,y)
(x,-y)
(-x,y)
4. Reflect the triangle over the x-axis and write the coordinates of W’Y’K’
W’ __________ Y’ ___________ K’ ________________
5. Reflect the original triangle over the y-axis and write the coordinates of
W”Y”K” W” _____________ Y” _____________ K” __________
A figure was reflected over an axis. The coordinates were A(3,6) and B(1,3) and C(3,1).
6. If the new image coordinates are A’(-3,6) and B’(-1,3) and C’(-3,1) , what was the axis of
reflection? _____________ What is the equation of that line? ________________
7. If the new image coordinates are A’(3,-6) and B’(1,-3) and C’(3,-1) , what was the axis of
reflection? _____________ What is the equation of that line? ________________
8. What is the equation for the line of reflection that reflects point P onto
P’ ?
9. What is the equation for the line of reflection that reflects point P’
onto P” ?
Reflections across the line y = x
The rule for a reflection over y = x
(𝒚, 𝒙)
is (𝒙, 𝒚) →
10. Draw the y = x line and
reflect the triangle on the
graph across the y = x line of
reflection. Connect W to W’,
and Y to Y’ and K to K’. What
are the slopes of the lines?
11. Reflect the triangle
across y = x
12. Reflect the triangle
13. Write the coordinates of
across y = x
the new points if the original
points are reflected across y= x
14. write the coordinates of the new
points if the original points are
reflected across y = x.
Reflections across the line y = -x
The rule for a reflection over y = -x is
(𝒙, 𝒚) →
(−𝒚, −𝒙)
15. Draw the y = -x line and
reflect the triangle on the
graph across the y = -x line
of reflection. Connect H to
H’ and E to E’ and V to V’.
What are the slopes of the
lines?
16. Reflect the triangle
Across y = -x
17. Reflect the triangle
across y = -x
18. Write the coordinates of
the new points if the original
points are reflected across y=-x.
19. Write the coordinates of the
new points if the original points
are reflected across y = -x.
20. What about other lines of reflection?
A. Draw a line between P and P’. What is the slope of the line
between P and P’?
B. Mark the midpoint between P and P’.
C. What is the slope that is perpendicular to the slope between P
and P’?
D. Start at the midpoint between P and P’ and use the perpendicular
slope and mark points for the line of reflection. Draw in the line.
E. What is the equation for the line of reflection that reflects point P onto P’?
21. Use the steps above to determine the line of reflection that reflects point P onto P”. What
is the equation for the line of reflection?
22.
Determine the equation of the line of reflection.
23.
24.
26.
27.
29.
30.
25.
28.
31.
32. Draw the line of reflection between the triangles
and write the equation of line of reflection.
1. E(2,-3) F(6,-3) G(5,-7)
2. E’(2,3) F’(6,3) G’(5,7)
33. Reflect the parallelogram over the line of
Reflection and label the image A’B’C’D’.
3. E”(-2,-3) F”(-6,-3) G”(-5,-7) 4. W”(-1,-4) Y’(-3,-2) K’(-2,0)
5. W”(1,4) Y”(3,2) K”(2,0) 6. y-axis and x=0 7. X-axis and y=0 8. X=0 9. Y=0 10. Slope of y=x line is 1 and the
slope of the line between the corresponding points of the image is -1. 13. Y’(-3,-5) X’(-1,0) W’(-5,-1) 14. I’(0,3)
H’(3,0) G’(2,1) 15. H’(-5,-5) E’(-4,-3) V’(-4.-5) 16. U’(-3,-1) W’(-2,-1) V’(-4,-4) 17. I’(4,-2) K’(3,3) J’(0,0) 18. Y’(3,5)
X’(1,0) W’(5,1) 19. I’(0,3) H’(-3,0) G’(-2.-1) 20. A. – ½ C. 2
1
1
2
2
E. y=2x-2 21. 𝑦 = 𝑥 −
22. Equation is y=3x+3
A’(5,-2) and equation is y=x and A’(1,2) 23. y=x 24. X=0 25. X=-3 26. Y=2 27. Y=0 28. y=x 29. Y=-1 30.
y=-x 31. y=-x 32. Y=x+5 32. A’(-2,-2) B’(-5,-1) C’(-4,-4) D’(-1,-5)