Question

The graph shows quadrilaterals ABCD and EFGH.
Quadrilateral ABCD has the points (-2, 4) for A, (-1, 6) for B, (3, 1) for C, and (2, 0) for D. Quadrilateral has the points (-5, -5) for E, (-4, -7) for F, (0, -2) for G, and (-1, -1) for H.
Are ABCD and EFGH congruent?
A. Yes, because a reflection across the y-axis followed by a translation 7 units down and 2 units to the left maps ABCD onto EFGH.
B. Yes, because a rotation 180 degrees counterclockwise about the origin maps ABCD onto EFGH.
C. Yes, because a reflection across the x-axis followed by a translation 3 units left and 1 unit down maps ABCD onto EFGH.
D. No, because there is no sequence of translations, rotations, and reflections that map ABCD onto EFGH.

Answer 1

C. Yes.

Reflect ABCD across the x-axis: A(-2,4) -> (-2,-4), B(-1,6) -> (-1,-6), C(3,1) -> (3,-1), D(2,0) -> (2,0).

Then translate 3 units left and 1 unit down (x - 3, y - 1):
(-2,-4) -> (-5,-5) = E,
(-1,-6) -> (-4,-7) = F,
(3,-1) -> (0,-2) = G,
(2,0) -> (-1,-1) = H.

Thus the given sequence of transformations maps ABCD onto EFGH, so they are congruent.