Question

The coordinates of the vertices of △PQR are P(1, 4) , Q(2, 2) , and R(−2, 1) . The coordinates of the vertices of △P′Q′R′ are P′(−1, 4) , Q′(−2, 2) , and R′(2, 1) .

Which statement correctly describes the relationship between △PQR and △P′Q′R′ ?

△PQR is congruent to △P′Q′R′ because you can map △PQR to △P′Q′R′ using a translation 2 units to the left, which is a rigid motion.
△PQR is congruent to △P′Q′R′ because you can map △PQR to △P′Q′R′ using a reflection across the y-axis, which is a rigid motion.
△PQR is not congruent to △P′Q′R′ because there is no sequence of rigid motions that maps △PQR to △P′Q′R′ .
△PQR is congruent to △P′Q′R′ because you can map △PQR to △P′Q′R′ using a reflection across the x-axis, which is a rigid motion.

Answer 1

B

Explanation:

Answer 2

The correct answer is B

EXPLANATION

If we analyse the coordinates carefully, you realize there is a mapping of

`(x,y)\rightarrow(-x,y)`

This is a reflection in the y-axis.

Since the transformation is a reflection, the shape is preserved. Therefore, the image triangle P'Q'R' of triangle

PQR are congruent.