Question

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

Explanation:

Step1: Recall the rotation rule

When a point \((x,y)\) is rotated \(270^{\circ}\) counter - clockwise about the origin, the new coordinates \((x',y')\) follow the rule \((x,y)\to(y,-x)\).

Step2: Apply the rule to the given point

Given \(P=(3,2)\), here \(x = 3\) and \(y=2\). Using the rule \((x,y)\to(y,-x)\), we substitute \(x = 3\) and \(y = 2\) into the formula. So the new \(x\) - coordinate of the image is \(y = 2\) and the new \(y\) - coordinate is \(-x=-3\).

Answer:

\(-3\)