Problem
3. Draw the preimage of a triangle with coordinates $T(2,1), U(0,-1)$, and $V(3,-3)$. Then, use the following coordinate plane to complete the following. ( 1 point each) a. Draw a reflection of the triangle across $y=x$. Label the new triangle as $\Delta T^{\prime} U^{\prime} V^{\prime}$. Mark the coordinates below: \[ \begin{array}{ll} \mathrm{T}^{\prime}( & ) \\ \mathrm{U}^{\prime}( & ) \\ \mathrm{V}^{\prime}( & ) \end{array} \] b. Rotate $\Delta T^{\prime} U^{\prime} V^{\prime} 90^{\circ}$ clockwise. Label the new figure as $\Delta T^{\prime \prime} U^{\prime \prime} V^{\prime \prime}$. Mark the coordinates below:
Solution
Step 1 ：Draw the preimage of a triangle with coordinates $T(2,1)$, $U(0,-1)$, and $V(3,-3)$.
Step 2 ：Reflect the triangle across the line $y=x$. This involves swapping the x and y coordinates of each point.
Step 3 ：The coordinates of the reflected triangle are $T^{\prime}(1, 2)$, $U^{\prime}(-1, 0)$, and $V^{\prime}(-3, 3)$.
Step 4 ：\[\boxed{\begin{array}{ll} T^{\prime}(1, 2) \\ U^{\prime}(-1, 0) \\ V^{\prime}(-3, 3) \end{array}}\]
