Question

if ( p = (-1,-1) ), find the image of ( p ) under the following rotation.
( 90^{circ} ) counterclockwise about the origin
( (1,?) )
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: Substitute the values of \(x\) and \(y\)

Here \(x = - 1\) and \(y=-1\).
Using the formula \((x',y')=(-y,x)\), we substitute \(y=-1\) and \(x = - 1\).
First, find \(x'\): \(x'=-y=-(-1) = 1\).
Second, find \(y'\): \(y'=x=-1\).

Answer:

\(-1\)