Question

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

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:

\((3,2)\) (corresponding to the option \((3,2)\))