Question

if p = (3, 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 rotation rule

The rule for a \(270^\circ\) counterclockwise rotation about the origin is \((x,y)\to(y, -x)\).

Step2: Apply the rule to \(P=(3,2)\)

For \(x = 3\) and \(y = 2\), applying the rule \((x,y)\to(y, -x)\), we get the new \(x\)-coordinate as \(y = 2\) and the new \(y\)-coordinate as \(-x=-3\). So the image of \(P\) is \((2, - 3)\). The green box is for the \(x\)-coordinate of the image, which is \(2\).

Answer:

2