Question

question 1 of 10
how many degrees has △abc been rotated counterclockwise about the origin?

Explanation:

Step1: Recall rotation rules

When a point \((x,y)\) is rotated counter - clockwise about the origin:

• A \(90^{\circ}\) rotation gives \((-y,x)\)
• A \(180^{\circ}\) rotation gives \((-x,-y)\)
• A \(270^{\circ}\) rotation gives \((y,-x)\)

Step2: Analyze the coordinates

Let's assume a general point \(P(x,y)\) in \(\triangle ABC\) and its image \(P'(y,-x)\) in \(\triangle A'B'C'\).
For example, if we consider the transformation of the vertices of the triangle. The transformation from \((x,y)\) to \((y, - x)\) is a \(270^{\circ}\) counter - clockwise rotation about the origin.

Answer:

$270^{\circ}$