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 \((-2,4)\).

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

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

Answer:

\((4,2)\)