Question

what is the image of the point $(-7,-8)$ after a rotation of $270^{circ}$ counterclockwise about the origin?

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

For the point \((-7,-8)\), here \(x=-7\) and \(y = - 8\).
Substitute \(x\) and \(y\) into the rule \((y,-x)\).
We get \(y=-8\) and \(-x=-(-7) = 7\).

Answer:

\((-8,7)\)