Question

if ( p=(2,-1) ), 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 formula

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

Step2: Apply the formula to the point \(P=(2,-1)\)

Here \(x = 2\) and \(y=-1\). Substituting into the formula, we get the new \(x\) - coordinate as \(y=-1\) and the new \(y\) - coordinate as \(-x=-2\).

Answer:

\(-1\)