Question

graph the image of square tuvw after a rotation 90° counterclockwise around the origin.

Explanation:

Step1: Recall rotation rule

The rule for a 90 - degree counter - clockwise rotation around the origin is $(x,y)\to(-y,x)$.

Step2: Identify original coordinates

Assume the coordinates of the vertices of square $TUVW$ are $T(x_T,y_T)$, $U(x_U,y_U)$, $V(x_V,y_V)$, $W(x_W,y_W)$. Let's say $T(5, - 7)$, $U(7, - 7)$, $V(7, - 5)$, $W(5, - 5)$.

Step3: Apply rotation rule

For point $T(5,-7)$: $(-(-7),5)=(7,5)$.
For point $U(7,-7)$: $(-(-7),7)=(7,7)$.
For point $V(7,-5)$: $(-(-5),7)=(5,7)$.
For point $W(5,-5)$: $(-(-5),5)=(5,5)$.

Step4: Graph new points

Plot the points $(7,5)$, $(7,7)$, $(5,7)$, $(5,5)$ on the coordinate - plane and connect them to form the rotated square.

Answer:

Graph the points obtained from the rotation rule $(x,y)\to(-y,x)$ for each vertex of the original square and connect them to form the new square.