Question

graph the image of c(-3, 0) after a rotation 180° counterclockwise around the origin.

Explanation:

Step1: Recall 180° rotation rule

For a point \((x, y)\) rotated 180° counterclockwise (or clockwise) around the origin, the rule is \((x, y) \to (-x, -y)\).

Step2: Apply the rule to point \(C(-3, 0)\)

Here, \(x = -3\) and \(y = 0\). Substituting into the rule: \(-x = -(-3)=3\), \(-y = -0 = 0\). So the image of \(C(-3, 0)\) after 180° rotation is \((3, 0)\).

Answer:

The image of \(C(-3, 0)\) after a 180° counterclockwise rotation around the origin is the point \((3, 0)\). To graph it, plot the point with \(x\)-coordinate 3 and \(y\)-coordinate 0 on the coordinate plane.