Question

the line segment shown is rotated 90° about the origin (counterclockwise) what are the new coordinates of point a? a (2,1) b (-2,1) c (-2 -1) d (1,2)

Explanation:

Step1: Determine the original coordinates of point A

From the graph, the original coordinates of point A are \((1, - 2)\).

Step2: Apply the rotation rule for a \(90^{\circ}\) counter - clockwise rotation about the origin

The rule for a \(90^{\circ}\) counter - clockwise rotation about the origin \((x,y)\to(-y,x)\).
Substitute \(x = 1\) and \(y=-2\) into the rule:
When \(x = 1\) and \(y=-2\), the new \(x\) - coordinate is \(-(-2)=2\) and the new \(y\) - coordinate is \(1\).

Answer:

A. \((2,1)\)