Question

rotate the polygon 180° about the origin.

Explanation:

Step1: Recall rotation rule

The rule for rotating a point $(x,y)$ 180 - degrees about the origin is $(x,y)\to(-x,-y)$.

Step2: Identify polygon vertices

Let's assume the vertices of the polygon are $(x_1,y_1),(x_2,y_2),\cdots$. For example, if one vertex is $(-5,8)$, after rotation, it becomes $(5, - 8)$. Do this for all vertices of the polygon.

Step3: Plot new - polygon

Connect the new vertices obtained from the previous step to form the rotated polygon.

Answer:

Plot the polygon with vertices obtained by applying the rule $(x,y)\to(-x,-y)$ to the original polygon's vertices.