Question

triangle abc is shown on the graph. what are the coordinates of the image of point b after the triangle is rotated 270° about the origin? (4, 2) (2, 4) (-4, -2) (-2, -4)

Explanation:

Step1: Determine the original coordinates of point B

From the graph, the coordinates of point B are \((- 4,2)\).

Step2: Apply the rotation rule for \(270^{\circ}\) counter - clockwise about the origin

The rule for a \(270^{\circ}\) counter - clockwise rotation about the origin \((x,y)\to(y, - x)\).
Substitute \(x=-4\) and \(y = 2\) into the rule:
When \(x=-4\) and \(y = 2\), the new \(x\) - coordinate is \(y = 2\) and the new \(y\) - coordinate is \(-x=-(-4)=4\).

Answer:

\((2,4)\)