Question

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

Explanation:

Step1: Analyze rotation effect

A $180^{\circ}$ rotation (clock - wise or counter - clockwise) changes the orientation of the triangle. After rotation, the relative position of the vertices with respect to the origin is reversed.

Step2: Analyze translation effect

Shifting 2 units to the right means adding 2 to the $x$ - coordinates of all vertices, and shifting 2 units up means adding 2 to the $y$ - coordinates of all vertices.
If we first rotate $\triangle ABC$ by $180^{\circ}$ (clockwise or counter - clockwise) about the origin, the orientation changes. Then, when we shift 2 units to the right and 2 units up, we get the correct position of $\triangle DEF$.

Answer:

$\triangle ABC$ was rotated $- 180^{\circ}$ (clockwise) or $180^{\circ}$ (counterclockwise), then shifted 2 units to the right and 2 units up.