Question

Note that WXYZ has vertices W(-1, 2), X(-5, 7), y(-1, -2), and Z (3, -7).
Answer the following to determine if the parallelogram is a rectangle, rhombus, square, or none of these.
(a) Find the slope of WZ and the slope of a side adjacent to WZ.
(b) Find the length of WZ and the length of a side adjacent to WZ. (Give exact answers, not decimal approximations.)
(c)What can we conclude about parallelogram WXYZ? Check all that apply.
-WXYZ is a rectangle
-WXYZ is a rhombus
-WXYZ is a square
-WXYZ is none of these.

Answer 1

a. Slope of WZ = -2.25; Slope of WX = 5

b. WZ = √97; WX = √41

c. WXYZ is not a rectangle, rhombus, nor a square. We can conclude that: D. WXYZ is none of these.

Slope of a Segment

Slope = change in y/change in x

Given:

W(-1, 2), X(-5, 7), Y(-1, -2), and Z (3, -7)

a. Slope of WZ and slope of WX:

Slope of WZ = (-7 - 2)/(3 -(-1)) = -2.25

Slope of WX = (7 - 2)/(-1 -(-1)) = 5

b. Use distance formula, $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$, to find WZ and WX:

$WZ = \sqrt{(3 - (-1))^2 + (-7 - 2)^2}\\\\\mathbf{WZ = \sqrt{97} }$

$WX = \sqrt{(-5 -(-1))^2 + (7 - 2)^2}\\\\\mathbf{WX = \sqrt{41} }$

c. The quadrilateral WXYZ have adjacent sides that are not perpendicular to each other and have different slopes and different lengths, so therefore, WXYZ is not a rectangle, rhombus, nor a square. We can conclude that: D. WXYZ is none of these.

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