Question

graph the image of rectangle tuvw after a rotation 180° counterclockwise around the origin.

Explanation:

Step1: Find the coordinates of the original rectangle

The coordinates of rectangle \(TUVW\) are \(T(5,1)\), \(U(8,1)\), \(V(8,8)\), \(W(5,8)\).

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 \(T(5,1)\): \((5,1)\to(- 5,-1)\)
For point \(U(8,1)\): \((8,1)\to(-8,-1)\)
For point \(V(8,8)\): \((8,8)\to(-8,-8)\)
For point \(W(5,8)\): \((5,8)\to(-5,-8)\)

Step3: Plot the new points

Plot the points \((-5,-1)\), \((-8,-1)\), \((-8,-8)\), \((-5,-8)\) on the coordinate plane and connect them to form the rotated rectangle.

Answer:

The new coordinates of the rectangle after \(180^{\circ}\) counter - clockwise rotation around the origin are \(T'(-5,-1)\), \(U'(-8,-1)\), \(V'(-8,-8)\), \(W'(-5,-8)\). Plot these points and connect them to get the image of the rotated rectangle.