Question

what is the location of the image of p(-4, 3) after a counterclockwise rotation of 90° about the origin? * (10 points) (-3, 4) (4, -3) (3, 4) (-3, -4)

Explanation:

Step1: Recall the rotation rule

When a point \((x,y)\) is rotated counter - clockwise by \(90^{\circ}\) about the origin, the transformation rule is \((x,y)\to(-y,x)\).

Step2: Apply the rule to the given point

For the point \(P(-4,3)\), here \(x = - 4\) and \(y = 3\).
Substitute \(x=-4\) and \(y = 3\) into the rule \((x,y)\to(-y,x)\).
We get \(-y=-3\) and \(x=-4\) (after rotation, the new \(x\) - coordinate is \(-y\) and the new \(y\) - coordinate is \(x\)). So the image point is \((-3,-4)\).

Answer:

\((-3, - 4)\)