Question

if ( p = (-3,5) ), find the image of ( p ) under the following rotation.
( 270^{circ} ) counterclockwise about the origin
( (5, ?) )
enter the number that belongs in the green box.

Explanation:

Step1: Recall rotation formula

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

Step2: Apply the formula

Given \(x=-3\) and \(y = 5\). Substitute into the formula: the new \(x\) - coordinate of the image is \(y = 5\), and the new \(y\) - coordinate is \(-x=-(-3)=3\).

Answer:

\(3\)