Answer:
- Q'(-3, 5)
- R'(-5, -1)
- S'(-2, 0)
- T'(0, 3)
Step-by-step explanation:
You want the coordinates of the vertices of QRST after it has been translated right 2 units, then reflected across the y-axis. The original coordinates are Q(1, 5), R(3, -1), S(0, 0), T(-2, 3).
Composition of Transformations
The problem statement is written as a composition of the transformations Ry and T(2,0). A composition of functions is generally executed right to left, meaning the translation will be done first, then the reflection.
Translation
The numbers in the translation vector are added to the coordinates:
(x, y) ⇒ (x+2, y+0)
Reflection
Reflection over the y-axis changes the sign of the x-coordinate:
(x, y) ⇒ (-x, y)
Application
Then the composition of transformations is ...
(x, y) ⇒ (-(x+2), y)
Q(1, 5) ⇒ Q'(-3, 5)
R(3, -1) ⇒ R'(-5, -1)
S(0, 0) ⇒ S'(-2, 0)
T(-2, 3) ⇒ T'(0, 3)
