Question

graph the image of v(-5, -1) after a rotation 270° counterclockwise around the origin.

Explanation:

Step1: Recall rotation rule

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

Step2: Apply the rule to \(V(-5,-1)\)

Here, \(x = - 5\) and \(y=-1\). Substituting into the rule, we get the new coordinates as \((y,-x)=(-1,-(-5))=(-1,5)\).

Answer:

The image of \(V(-5,-1)\) after a \(270^\circ\) counterclockwise rotation around the origin is the point \((-1,5)\). To graph it, plot the point with \(x\)-coordinate \(-1\) and \(y\)-coordinate \(5\) on the coordinate plane.