Question

follow the guided instructions below to rotate the figure 270° 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

The rule for a 270 - counter - clockwise rotation about the origin $(x,y)\to(y, - x)$.

Step2: Identify vertices

Let the vertices of the triangle be $(x_1,y_1),(x_2,y_2),(x_3,y_3)$. For example, if one vertex is $(- 8,7)$, after 270 - counter - clockwise rotation about the origin, using the rule $(x,y)\to(y, - x)$, it becomes $(7,8)$. Do this for all vertices of the triangle.

Step3: Draw the circle

The center of the circle is at the origin $(0,0)$. To ensure one vertex of the figure is on the circle, measure the distance from the origin to one of the vertices of the original or rotated triangle. This distance $r=\sqrt{x^{2}+y^{2}}$. For a vertex $(x,y)$ of the triangle, draw a circle with the equation $x^{2}+y^{2}=r^{2}$ where $r$ is the distance from the origin to that vertex.

Answer:

After rotating the triangle 270° counter - clockwise about the origin using the rule $(x,y)\to(y, - x)$ for each vertex and drawing a circle centered at the origin with radius equal to the distance from the origin to one of the vertices of the triangle.