Question

trapezoid g h j k was rotated 180° about the origin to determine the location of g h j k, as shown on the graph. what are the coordinates of pre - image point h? \\(\boldsymbol{(2, 3)}\\) \\(\boldsymbol{(-2, 3)}\\) \\(\boldsymbol{(3, 2)}\\) \\(\boldsymbol{(3, -2)}\\)

Explanation:

Step1: Recall 180° rotation rule

A 180° rotation about the origin transforms a pre-image point $(x,y)$ to image point $(-x,-y)$. To reverse this, the pre-image of a point $(a,b)$ is $(-a,-b)$.

Step2: Identify image point H'

From the graph, the image point $H'$ is $(-2, 3)$.

Step3: Calculate pre-image H

Apply the reverse rotation: pre-image $H = -(-2), -(3) = (2, -(-3))$ → $H=(2, 3)$.

Answer:

(2, 3)