Question

determine the congruence transformation used on △abc that resulted in △def. (1 point) △abc was reflected across the y - axis, then shifted 2 units to the right and 2 units up. △abc was shifted 2 units to the right and 2 units up, then rotated 180° (counterclockwise). △abc was shifted 2 units to the left and 2 units up, then reflected across the y - axis. △abc was rotated - 180° (clockwise) or 180° (counterclockwise) then shifted 2 units to the right and 2 units up.

Explanation:

Step1: Analyze reflection

Check the orientation of the triangles. The x - coordinates of corresponding points of $\triangle ABC$ and $\triangle DEF$ have opposite signs, which indicates a reflection across the y - axis.

Step2: Analyze translation

After reflection, we can see that each point of the reflected triangle is moved 2 units to the right and 2 units up to get $\triangle DEF$. For example, if we take point A(-2,3), after reflection across y - axis it becomes (2,3) and then after translation 2 units right and 2 units up it moves to the corresponding point of $\triangle DEF$.

Answer:

$\triangle ABC$ was reflected across the y - axis, then shifted 2 units to the right and 2 units up.