Question

follow the guided instructions below to rotate the figure 90° 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 clockwise rotation about the origin, the transformation rule for a point $(x,y)$ is $(x,y)\to(y, - x)$.

Step2: Identify vertices of the triangle

Let the vertices of the triangle be $(x_1,y_1)$, $(x_2,y_2)$ and $(x_3,y_3)$. Assume the vertices are $(-2,-3)$, $(-2, - 5)$ and $(-1,-5)$.

Step3: Apply rotation rule

For the point $(-2,-3)$: Using the rule $(x,y)\to(y, - x)$, we get $(-3,2)$.
For the point $(-2,-5)$: Using the rule $(x,y)\to(y, - x)$, we get $(-5,2)$.
For the point $(-1,-5)$: Using the rule $(x,y)\to(y, - x)$, we get $(-5,1)$.

Step4: Plot the new - rotated triangle

Plot the points $(-3,2)$, $(-5,2)$ and $(-5,1)$ on the coordinate - plane and connect them to form the rotated triangle.

Answer:

Plot the points obtained from the rotation rule $(y, - x)$ for each vertex of the original triangle and connect them to get the 90 - degree clockwise rotated triangle about the origin.