Question

write the coordinates of the vertices after a rotation 180° counterclockwise around the origin.

Explanation:

Step1: Find the original coordinates

From the graph, the coordinates of \(U\) is \((-9,-3)\), \(V\) is \((0,-3)\) and \(W\) is \((-9,-10)\).

Step2: Apply the rotation rule

The rule for a \(180^{\circ}\) counter - clockwise rotation around the origin is \((x,y)\to(-x,-y)\).
For point \(U(-9,-3)\):
\((-9,-3)\to(9,3)\)
For point \(V(0,-3)\):
\((0,-3)\to(0,3)\)
For point \(W(-9,-10)\):
\((-9,-10)\to(9,10)\)

Answer:

The coordinates of \(U'\) is \((9,3)\), \(V'\) is \((0,3)\) and \(W'\) is \((9,10)\)