Question

graph the image of \\( \triangle qrs \\) after a rotation \\( 180 ^ { \circ } \\) counterclockwise around the origin.

Explanation:

Step1: Find the coordinates of the original points

From the graph, we can see that the coordinates of \(S\) are \((-7,0)\), the coordinates of \(Q\) are \((-5,-3)\), and the coordinates of \(R\) are \((-1,-3)\).

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 \(S(-7,0)\):
\((-7,0)\to(7,0)\)
For point \(Q(-5,-3)\):
\((-5,-3)\to(5,3)\)
For point \(R(-1,-3)\):
\((-1,-3)\to(1,3)\)

Step3: Plot the new points

Plot the points \((7,0)\), \((5,3)\), and \((1,3)\) on the coordinate plane and connect them to form the image of \(\triangle QRS\) after the rotation.

Answer:

The coordinates of the vertices of the rotated triangle are \(S'(7,0)\), \(Q'(5,3)\), and \(R'(1,3)\). Plot these points and connect them.