Question

if ( p=(2,-1) ), find the image of ( p ) under the following rotation.
( 270^{circ} ) counterclockwise about the origin
( (-1, ? ) )
enter the number that belongs in the green box.

Explanation:

Step1: Recall the rotation rule

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

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

Here \(x = 2\) and \(y=-1\). Using the rule \((x,y)\to(y,-x)\), we substitute \(x\) and \(y\) values.
We get \(y=-1\) and \(-x=-2\).

Answer:

\(-2\)