Note that WXYZ has vertices W(3,2),X(1,-3),Y(-5,-2) and Z(-3,3) Complete the following to determine if WXYZ is a parallelogram. (a) Find the length of overline (WX) and the length of overline (YZ) Give exact answers (not decimal approximations). Length of overline (WX) square Length of overline (YZ) square

## Step 1<br />To determine if the quadrilateral WXYZ is a parallelogram, we need to check if the opposite sides are equal in length. In this case, we are asked to find the lengths of the line segments WX and YZ.<br /><br />## Step 2<br />We can use the distance formula to find the lengths of these line segments. The distance formula is given by:<br />### \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)<br /><br />## Step 3<br />For line segment WX, we substitute the coordinates of points W and X into the distance formula:<br />### \(d_{WX} = \sqrt{(1 - 3)^2 + (-3 - 2)^2}\)<br /><br />## Step 4<br />Similarly, for line segment YZ, we substitute the coordinates of points Y and Z into the distance formula:<br />### \(d_{YZ} = \sqrt{(-3 - (-5))^2 + (3 - (-2))^2}\)<br /><br />## Step 5<br />After calculating these lengths, we can compare them to see if they are equal. If they are, then WXYZ is a parallelogram.