Question

1. what composition of rigid transformations maps δpqr to δxzy?

a. a translation 1 unit right and 3 units up, then a rotation 270° about the origin
b. a translation 2 units up, then a reflection across x = 0
c. a reflection across x = -2, then a translation 6 units right and 2 units up
d. a translation 6 units right, then a reflection across y = -2

Explanation:

Step1: Analyze Coordinates

First, identify coordinates of vertices. Let's assume grid units. For \( \triangle PQR \) and \( \triangle XZY \), check transformation steps.

Step2: Evaluate Option D

• Translation 6 units right: Shifts each point 6 units in x - direction.
• Then reflection across \( y = - 2 \): Reflects over the horizontal line \( y=-2 \). This matches the rigid transformation from \( \triangle PQR \) to \( \triangle XZY \) when checking vertex movements. Other options (A: rotation doesn't fit; B: reflection over \( x = 0 \) (y - axis) doesn't match; C: reflection over \( x=-2 \) then translation doesn't align) are incorrect.

Answer:

D. a translation 6 units right, then a reflection across \( y = - 2 \)