Question

how many degrees has \\( \triangle abc \\) been rotated counterclockwise about the origin?
a. \\( 90 ^ { \circ } \\)
b. \\( 360 ^ { \circ } \\)
c \\( 180 ^ { \circ } \\)

Explanation:

Step1: Analyze rotation rules

A \( 90^{\circ} \) counter - clockwise rotation about the origin changes a point \((x,y)\) to \((-y,x)\).

Step2: Check coordinates

For example, if we assume a general point in \(\triangle ABC\) and its image in \(\triangle A'B'C'\), the transformation fits the \(90^{\circ}\) counter - clockwise rotation rule.
A \( 180^{\circ}\) rotation would change \((x,y)\) to \((-x,-y)\) which does not match. A \(360^{\circ}\) rotation would map the figure onto itself (no net change in position relative to original), which is not the case here. So the rotation is \(90^{\circ}\) counter - clockwise.

Answer:

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