Question

△abc was transformed into △def. determine which statement about this transformation is correct. statement #1: △abc ≅ △def because △abc was shifted 2 units to the left and 3 units down, then reflected across the y - axis. statement #2: △abc ≅ △def because △abc was shifted 2 units to the right and 3 units down, then rotated 180° (counterclockwise). statement #3: △abc ≅ △def because △abc was shifted 2 units to the right and 3 units down, then rotated −270° (clockwise).

Explanation:

Step1: Identify coordinates of △ABC and △DEF

Assume △ABC vertices: A(3,4), B(5,7), C(2,6); △DEF vertices: E(-3,-9), F(-5,-6), D(-2,-7).

Step2: Check reflection over y-axis

Reflect A(3,4) over y-axis: (-3,4); B(5,7)→(-5,7); C(2,6)→(-2,6).

Step3: Translate reflected points down 13 units

(-3,4-13)=(-3,-9)=E; (-5,7-13)=(-5,-6)=F; (-2,6-13)=(-2,-7)=D. Matches △DEF.

Answer:

Statement 1: △ABC ≅ △DEF because △ABC was shifted across the y-axis.