Question

to prove the triangles are congruent, which of the following rigid motions would map △ghj to △znp? (1 point) o translation along the vector, mapping point j to point p, then rotation 90° (counter - clockwise) about point j o translation along the vector, mapping point g to point n, then rotation - 90° (clockwise) about point g o translation along the vector, mapping point j to point p, then rotation - 90° (clockwise) about point j o rotation - 90° (clockwise) about point j, then translation along the vector, mapping point h to point z

Explanation:

Step1: Analyze translation

Translation is a rigid - motion that moves every point of a figure by the same distance in a given direction. Mapping point $J$ to point $P$ by translation is a valid first step as it aligns one of the vertices of the two triangles.

Step2: Analyze rotation

A rotation of $- 90^{\circ}$ (clock - wise) about point $J$ after translating $J$ to $P$ will re - orient $\triangle GHJ$ to match the orientation of $\triangle ZNP$. A $-90^{\circ}$ (clock - wise) rotation about a point changes the orientation of the figure in a way that can make the two triangles coincide.

Answer:

translation along the vector, mapping point $J$ to point $P$, then rotation $-90^{\circ}$ (clockwise) about point $J$