The image of the triangle is the result of the following rigid transformations: 1) Translation 6 units down, 2) Reflection about y-axis. (Correct choice: D)
How to determine the rigid transformation between a triangle and its image
In this problem we find the case of the representation of a triangle and its image, whose sequence of rigid transformation must be found. By direct inspection, we notice that image is the result of the following rigid transformations:
- Translation 6 units down.
- Reflection about y-axis.
Now we prove the rigid transformations mentioned: Q(x, y) = (- 4, 5), R(x, y) = (- 2, 2), S(x, y) = (- 5, 2)
Step 1: Translation.
Q(x, y) = (- 4, 5) → Q'(x, y) = (- 4, - 1)
R(x, y) = (- 2, 2) → R'(x, y) = (- 2, - 4)
S(x, y) = (- 5, 2) → S'(x, y) = (- 5, - 4)
Step 2: Reflection.
Q'(x, y) = (- 4, - 1) → Q''(x, y) = (4, - 1)
R'(x, y) = (- 2, - 4) → R''(x, y) = (2, - 4)
S'(x, y) = (- 5, - 4) → S''(x, y) = (5, - 4)