Question

if p = (8, 2), find the image of p under the following rotation. 270° counterclockwise about the origin (?, ) 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 given point

Given \(P=(8,2)\), here \(x = 8\) and \(y=2\).
After applying the rule \((x,y)\to(y,-x)\), we substitute \(x = 8\) and \(y = 2\) into the formula.
We get the new \(x\) - coordinate as \(y = 2\) and the new \(y\) - coordinate as \(-x=-8\).

Answer:

\(2\)