Question

The coordinates for a quadrilateral are W(-8, -3), X(-7, 7), Y(3, 6), and Z(2, -4). Determine the type of quadrilateral.

a. Rhombus
b. Parallelogram
c. Rectangle
d. Square

Answer 1

To determine the type of quadrilateral, we need to examine the properties of the given coordinates.

Step-by-step explanation:

To determine the type of quadrilateral, we need to examine the properties of the given coordinates. A parallelogram is a quadrilateral whose opposite sides are parallel. Therefore, we need to check if the slopes of the sides are equal. Using the formula for slope, we can calculate the slopes of the sides WX, XY, YZ, and ZW.

1. For the slope of WX: m = (Yy - Xy) / (Yx - Xx) = (6 - 7) / (3 + 7) = -1 / 10
2. For the slope of XY: m = (Yy - Xy) / (Yx - Xx) = (6 - 7) / (3 - (-7)) = -1 / 10
3. For the slope of YZ: m = (Zy - Yy) / (Zx - Yx) = (-4 - 6) / (2 - 3) = -10 / -1 = 10
4. For the slope of ZW: m = (Zy - Wx) / (Zx - Wx) = (-4 - (-3)) / (2 - (-8)) = -1 / 10

Since the slopes of the opposite sides WX and YZ are equal (-1/10 = -1/10) and the slopes of the opposite sides XY and ZW are equal (10 = 10), we can conclude that the given coordinates form a parallelogram.