Question

graph the image of u(7, 9) after a rotation 90° counterclockwise around the origin.

Explanation:

Step1: Recall rotation rule

For a point \((x, y)\) rotated \(90^\circ\) counterclockwise around the origin, the new coordinates \((x', y')\) are given by \((-y, x)\).

Step2: Apply rule to \(U(7, 9)\)

Here, \(x = 7\) and \(y = 9\). So, \(x'=-y=-9\) and \(y' = x = 7\). Thus, the image of \(U(7, 9)\) after \(90^\circ\) counterclockwise rotation is \((-9, 7)\). To graph this, plot the point with \(x\)-coordinate \(-9\) and \(y\)-coordinate \(7\) on the coordinate plane.

Answer:

The image of \(U(7, 9)\) after \(90^\circ\) counterclockwise rotation around the origin is the point \((-9, 7)\), which should be plotted on the coordinate plane at \(x = -9\), \(y = 7\).