Question

what are the coordinates of the point (2,-3) after a counterclockwise rotation of 90° about the origin? (3,2) (-2,3) (-3,-2) (-3,2)

Explanation:

Step1: Recall rotation rule

For a point \((x,y)\) rotated \(90^\circ\) counterclockwise about the origin, the new coordinates \((x',y')\) are given by \((-y,x)\).

Step2: Apply the rule to \((2,-3)\)

Here, \(x = 2\) and \(y=-3\). Substituting into the rule: \(x'=-y=-(-3) = 3\) and \(y'=x = 2\). So the new coordinates are \((3,2)\).

Answer:

(3,2)