Question

graph the image of \\( \triangle stu \\) after a rotation \\( 270 ^ { \circ } \\) counterclockwise around the origin.

Explanation:

Step1: Determine the coordinates of the original points

Assume \(S=(0,2)\), \(T=(0,5)\), \(U=(9,7)\)

Step2: Apply the rotation formula

The formula for a \(270^{\circ}\) counter - clockwise rotation about the origin is \((x,y)\to(y, - x)\)
For point \(S=(0,2)\):
\(S'=(2,0)\)
For point \(T=(0,5)\):
\(T'=(5,0)\)
For point \(U=(9,7)\):
\(U'=(7, - 9)\)

Step3: Plot the new points

Plot \(S'(2,0)\), \(T'(5,0)\), \(U'(7, - 9)\) on the coordinate plane and connect them to form \(\triangle S'T'U'\)

Answer:

Plot the points \(S'(2,0)\), \(T'(5,0)\), \(U'(7, - 9)\) and connect them.