Question

figure p was rotated about the origin (0, 0) by 180°. which figure is the image of p? choose 1 answer:

Explanation:

Step1: Recall rotation rule

When a point $(x,y)$ is rotated 180 - degrees about the origin, the new - point is $(-x,-y)$. For a figure, we apply this rule to all its vertices.

Step2: Analyze the orientation

A 180 - degree rotation about the origin changes the orientation of the figure such that it is flipped across the origin. The figure will be in the quadrant opposite to the original one.

Step3: Check the options

Option A: The figure in option A is not a 180 - degree rotation of $P$ about the origin.
Option B: The figure in option B is not a 180 - degree rotation of $P$ about the origin.
Option C: When we apply the 180 - degree rotation rule to each vertex of figure $P$, the resulting figure matches option C.
Option D: The figure in option D is not a 180 - degree rotation of $P$ about the origin.

Answer:

C.