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′ ?

A) △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.

B) △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.

C) △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.

D) △PQR is not congruent to △P′Q′R′ because there is no sequence of rigid motions that maps △PQR to △P′Q′R′ .

Answer 1

ANSWER

The correct answer is option B

EXPLANATION

When we analyse carefully we can see that PQR is mapped on to P'Q'R' by the rule

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

$P(1,4)\rightarrow P'(-1,4)$

$Q(2,2)\rightarrow Q'(-2,2)$

$R(-2,1)\rightarrow R'(2,2)$

That is to say the x-coordinates are negated. Hence y-axis is the mirror line.

Since reflection is a rigid motion, the two triangles are congruent. That means the two triangles PQR and P'Q'R' are equal in all respect.

See graph in attachment.