The problem asks to find the slope of line segment $TQ$ and the slope of line segment $SR$ given the vertices of quadrilateral $QRST$: $Q(3, 2)$, $R(1, -6)$, $S(-1, -6)$, and $T(-3, 2)$.

1. Problem Description

The problem asks to find the slope of line segment $TQ$ and the slope of line segment $SR$ given the vertices of quadrilateral $QRST$: $Q(3, 2)$, $R(1, -6)$, $S(-1, -6)$, and $T(-3, 2)$.

2. Solution Steps

To find the slope of a line segment, we use the formula:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

For the slope of $TQ$, we have $T(-3, 2)$ and $Q(3, 2)$.

$m_{TQ} = \frac{2 - 2}{3 - (-3)} = \frac{0}{6} = 0$

For the slope of $SR$, we have $S(-1, -6)$ and $R(1, -6)$.

$m_{SR} = \frac{-6 - (-6)}{1 - (-1)} = \frac{0}{2} = 0$

3. Final Answer

Slope of $TQ$: 0

Slope of $SR$: 0