Question

graph the image of square tuvw after a rotation 180° counter - clockwise around the origin.

Explanation:

Step1: Recall rotation rule

The rule for a 180 - degree counter - clockwise rotation around the origin is $(x,y)\to(-x,-y)$.

Step2: Identify vertices of square TUVW

Let's assume the coordinates of the vertices of square TUVW are $T(x_1,y_1)$, $U(x_2,y_2)$, $V(x_3,y_3)$, $W(x_4,y_4)$. For example, if $T(- 8,2)$, $U(-6,2)$, $V(-6,4)$, $W(-8,4)$.

Step3: Apply rotation rule to each vertex

For vertex $T(-8,2)$, after rotation, $T'=(8, - 2)$. For $U(-6,2)$, $U'=(6,-2)$. For $V(-6,4)$, $V'=(6,-4)$. For $W(-8,4)$, $W'=(8,-4)$.

Step4: Plot new vertices

Plot the new vertices $T'$, $U'$, $V'$, $W'$ on the coordinate - plane and connect them to form the rotated square.

Answer:

Graph the square with vertices obtained by applying the $(x,y)\to(-x,-y)$ rule to the original square's vertices.