Question

follow the guided instructions below to rotate the figure 180° clockwise about the origin. click and drag to draw a line through the yellow center and the vertex on the circle.

Explanation:

Step1: Recall rotation rule

For a 180 - degree clockwise rotation about the origin $(0,0)$, the transformation rule for a point $(x,y)$ is $(x,y)\to(-x,-y)$.

Step2: Identify vertices of the figure

Let's assume the vertices of the original figure are $(x_1,y_1),(x_2,y_2),\cdots$.

Step3: Apply the rotation rule

For each vertex $(x_i,y_i)$ of the original figure, the new vertex after 180 - degree clockwise rotation about the origin will be $(-x_i,-y_i)$.

Step4: Plot the new figure

Connect the new vertices $(-x_i,-y_i)$ to form the rotated figure.

Since this is a graphical task and we can't actually draw in this text - based format, the general steps to rotate a figure 180 degrees clockwise about the origin are as above.

Answer:

Follow the steps: 1. Use the rule $(x,y)\to(-x,-y)$ for each vertex of the figure. 2. Plot the new vertices. 3. Connect the new vertices to form the rotated figure.