Question

if ( p=(3,2) ), find the image of ( p ) under the following rotation.
( 270^{circ} ) counterclockwise about the origin
( (?,) )
enter the number that belongs in the green box.

Explanation:

Step1: Recall rotation formula

When a point \((x,y)\) is rotated \(270^{\circ}\) counter - clockwise about the origin, the transformation formula is \((x,y)\to(y, - x)\).

Step2: Apply the formula

Given \(P=(3,2)\), here \(x = 3\) and \(y=2\). Substitute into the formula \((x,y)\to(y,-x)\). We get the new \(x\) - coordinate as \(y = 2\) and the new \(y\) - coordinate as \(-x=-3\).

Answer:

\(2\)