Question

graph the image of $\triangle tuv$ after a rotation $180^{circ}$ counterclockwise around the origin.

Explanation:

Step1: Identify original coordinates

From the graph:
$T=(2, 6)$, $U=(2, 7)$, $V=(10, 5)$

Step2: Apply 180° rotation rule

A 180° counterclockwise rotation around the origin transforms a point $(x,y)$ to $(-x,-y)$.
For $T$: $(-2, -6)$
For $U$: $(-2, -7)$
For $V$: $(-10, -5)$

Step3: Plot new points

Plot $T'=(-2, -6)$, $U'=(-2, -7)$, $V'=(-10, -5)$ and connect them to form $\Delta T'U'V'$.

Answer:

The vertices of the rotated triangle are $T'(-2, -6)$, $U'(-2, -7)$, $V'(-10, -5)$. When plotted and connected, this forms the 180° counterclockwise rotation of $\Delta TUV$ around the origin.