Question

if ( p = (-3, 5) ), 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 the rotation rule

The rule for a \(270^{\circ}\) counter - clockwise rotation about the origin is \((x,y)\to(y, - x)\).

Step2: Apply the rule to the point \(P(-3,5)\)

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

Answer:

\(5\)