Question

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

Explanation:

Step1: Analyze rotation

A 180 - degree rotation (clockwise or counter - clockwise) changes the sign of both the x and y coordinates of each point. For example, if a point $(x,y)$ is rotated 180 degrees about the origin, it becomes $(-x,-y)$.

Step2: Analyze translation

A shift of 2 units to the right means adding 2 to the x - coordinate of each point, and a shift of 2 units up means adding 2 to the y - coordinate of each point.

Step3: Check the order

If we first rotate $\triangle ABC$ 180 degrees about the origin and then perform the translation (2 units right and 2 units up), we can match the vertices of $\triangle ABC$ to $\triangle DEF$.

Answer:

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