Question

follow the guided instructions below to rotate the figure 90° counter - clockwise about the origin. draw a circle centered at the center of rotation, such that one of the vertices of the figure is on the circle.

Explanation:

Step1: Recall rotation rule

For a 90 - degree counter - clockwise rotation about the origin, the transformation rule for a point $(x,y)$ is $(x,y)\to(-y,x)$.

Step2: Identify vertices

Suppose the vertices of the triangle are $(x_1,y_1),(x_2,y_2),(x_3,y_3)$.

Step3: Apply rotation rule

The new vertices after 90 - degree counter - clockwise rotation will be $(-y_1,x_1),(-y_2,x_2),(-y_3,x_3)$.

Step4: Plot new figure

Plot the new triangle with the rotated vertices on the coordinate plane.

Answer:

The new figure after 90 - degree counter - clockwise rotation about the origin is obtained by applying the rule $(x,y)\to(-y,x)$ to each vertex of the original figure and then connecting the new vertices.