Question

what is the image of the point $(4,-8)$ after a rotation of $270^{circ}$ counterclockwise about the origin?

Explanation:

Step1: Recall the rotation rule

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

Step2: Apply the rule to the given point

For the point \((4,-8)\), substitute \(x = 4\) and \(y=-8\) into the rule. We get \((4,-8)\to(-8,-4)\).

Answer:

$(-8, -4)$