Question

graph the image of n(9, 10) after a rotation 270° counterclockwise around the origin.

Explanation:

Step1: Recall rotation rule

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

Step2: Apply the rule to point \(N(9,10)\)

For point \(N(9,10)\), \(x = 9\) and \(y = 10\). Using the rule \((x,y)\to(y, -x)\), we substitute \(x = 9\) and \(y = 10\). So the new \(x\)-coordinate is \(y = 10\) and the new \(y\)-coordinate is \(-x=- 9\). Thus, the image of \(N(9,10)\) after a \(270^\circ\) counterclockwise rotation around the origin is \((10,-9)\).

Answer:

The image of \(N(9,10)\) after a \(270^\circ\) counterclockwise rotation around the origin is the point with coordinates \((10, - 9)\). To graph it, locate the point where \(x = 10\) and \(y=-9\) on the coordinate plane.