Question

question 3 of 10
how many degrees has \\( \triangle a b c \\) been rotated counterclockwise about the
origin?

Explanation:

Step1: Recall rotation rules

When a point \((x,y)\) is rotated \(180^{\circ}\) counter - clockwise about the origin, it becomes \((-x,-y)\).

Step2: Check coordinates

Assume \(A(x_1,y_1)\), \(B(x_2,y_2)\), \(C(x_3,y_3)\) and \(A'(x_1',y_1')\), \(B'(x_2',y_2')\), \(C'(x_3',y_3')\). If \(x_1'=-x_1\), \(y_1'=-y_1\); \(x_2'=-x_2\), \(y_2'=-y_2\); \(x_3'=-x_3\), \(y_3'=-y_3\) (by observing the graph, the relationship between original and image points satisfies the \(180^{\circ}\) rotation rule about the origin).
So \(\triangle ABC\) is rotated \(180^{\circ}\) counter - clockwise about the origin.

Answer:

A. \(180^{\circ}\)