Transformations. Need help immediately.

Question

Which sequence of transformations will map figure Q onto figure Q′?

Two congruent trapezoids figure Q and figure Q prime are drawn on a coordinate grid. Figure Q has vertices at (-9, 2), (-6, 4) (-4,4) and (-2,2). Figure Q prime has vertices at (2,2) (4,4) (6,4) and (9,2).

A. Translation of (x, y + 2), reflection over x = 1, and 180° rotation about the origin.

B. Translation of (x, y − 2), reflection over x = 1, and 180° rotation about the origin.

C. Translation of (x, y − 2), reflection over y = 1, and 180° rotation about the origin.

D. Translation of (x, y + 2), reflection over y = 1, and 180° rotation about the origin.

Answer 1

Take the first point of Q, (-9,2). Reflection over x = 1 would push the new x value 10 units to the right of x = 1, which is x = 11, and 180 rotation would make x = -11. That's not in Q prime, so it must be reflection over

y = 1, choice C or D.

Looking at C, translation of (-9,2) becomes (-9,0), reflection over y = 1 gives (-9,2), and rotation gives (9,-2)

Again, not in Q prime.

Looking at D, translation of (-9,2) becomes (-9,4), reflection over y = 1 gives (-9,-2), and rotation gives (9,2).

This is in Q prime. You could assume the other points will also check out. Or test them out:

(-6,4) (-6,6) (-6,-4) (6,4)

This works also.

Essentially, the x value in Q becomes -x in Q prime. The remaining points will do likewise with x, and the y values are the same as in the first 2 points of Q. So D is correct.