We are given a quadrilateral $QRST$. We are asked to find the lengths of the sides $TS$ and $QR$. We are given the coordinates of $T(-3, 2)$. From the figure, we can determine the coordinates of the other vertices.

1. Problem Description

We are given a quadrilateral $QRST$.

We are asked to find the lengths of the sides $TS$ and $QR$. We are given the coordinates of $T(-3, 2)$. From the figure, we can determine the coordinates of the other vertices.

2. Solution Steps

From the graph:

$Q(1, 3)$

$R(1, -1)$

$S(-3, -1)$

$T(-3, 2)$

To find the length of $TS$, we use the distance formula:

$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$.

$TS = \sqrt{(-3 - (-3))^2 + (2 - (-1))^2}$

$TS = \sqrt{(0)^2 + (3)^2}$

$TS = \sqrt{0 + 9}$

$TS = \sqrt{9}$

$TS = 3$

To find the length of $QR$, we use the distance formula:

$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$.

$QR = \sqrt{(1 - 1)^2 + (3 - (-1))^2}$

$QR = \sqrt{(0)^2 + (4)^2}$

$QR = \sqrt{0 + 16}$

$QR = \sqrt{16}$

$QR = 4$

3. Final Answer

Length of $TS$: 3

Length of $QR$: 4