Question

if ( p = (-1,-1) ), find the image of ( p ) under the following rotation.
( 90^{circ} ) counterclockwise about the origin
( (?,) )
enter the number that belongs in the green box.

Explanation:

Step1: Recall the rotation formula

When a point \((x,y)\) is rotated \(90^{\circ}\) counter - clockwise about the origin, the new coordinates \((x',y')\) are given by the formula \((x',y')=(-y,x)\).

Step2: Apply the formula to the given point

For the point \(P=(-1,-1)\), here \(x = - 1\) and \(y=-1\).
Substitute \(x\) and \(y\) into the formula: \(x'=-y=-(-1) = 1\) and \(y'=x=-1\).

Answer:

\(1\)