Question

question 5 of 25
how many degrees has \\( \triangle a b c \\) been rotated counterclockwise about the origin?

Explanation:

Step1: Determine rotation direction and degree

When a figure is rotated counter - clockwise about the origin, we can use the property of rotation. For a \(90^{\circ}\) counter - clockwise rotation about the origin \((x,y)\to(-y,x)\).
If we assume a general point \(P(x,y)\) in \(\triangle ABC\) and its corresponding point \(P'( - y,x)\) in \(\triangle A'B'C'\) (by observing the coordinate transformation of vertices \(A\) to \(A'\), \(B\) to \(B'\), \(C\) to \(C'\) in the graph), we can verify the rotation rule.
Another way is to use the concept of angle between the original and rotated position of a line segment (e.g., consider a line segment from the origin to a vertex of \(\triangle ABC\) and its image in \(\triangle A'B'C'\)). The angle between them is \(90^{\circ}\) as per the rotation property.

Answer:

A. \(90^{\circ}\)