Question

The coordinates of the vertices of APQR are (-2, 2), (-6, -2), and (-6, 5). The coordinates of the vertices of AP’Q’R’ are (-2, 2), (-6, -2), and (-6, 5). This transformation can be expressed as (x, y) > (x, -y). Is APQR congruent to AP’Q’R’? Why or why not?

a) Yes, because the y-coordinates are negated.
b) No, because the x-coordinates are negated.
c) Yes, because both x and y coordinates are negated.
d) No, because neither x nor y coordinates are negated.

Answer 1

APQR and AP'Q'R' are congruent because their coordinates are identical, signifying that neither x nor y coordinates are negated in the transformation.

Step-by-step explanation:

The question asks whether the figures APQR and AP'Q'R' are congruent when applying the transformation (x, y) to (x, -y). Given the coordinates of the vertices for both figures are (-2, 2), (-6, -2), and (-6, 5), we can see that the transformation does not change the coordinates at all. Thus, APQR and AP'Q'R' have identical coordinates, which means the transformation does not alter the figure, and they are naturally congruent.

Since the coordinates for both figures are the same, the correct option is d) No, because neither x nor y coordinates are negated. The y-coordinates are not negated since they remain the same in both figures.