contestada

Item 15 Question 1 Show that quadrilateral WXYZ with vertices W(−1,6), X(2, 8), Y(1, 0), and Z(−2,−2) is a parallelogram by finding the indicated slopes and side lengths. Item 15 Question 1 Show that quadrilateral WXYZ with vertices W(−1,6), X(2, 8), Y(1, 0), and Z(−2,−2) is a parallelogram by finding the indicated slopes and side lengths.

Respuesta :

Answer:

Multiple answers

Step-by-step explanation:

A parallelogram is a flat shape that has four sides. The two sets of opposite sides are parallel and of equal length to each other.

To prove that our figure is a parallelogram we first get the slope of our sides.

The formule we use to get the slope is:

m = [tex]\frac{y-y1}{x-x1}[/tex]

  1. first we have the W-Z side that it's supossed to be parallel to X-Y side

if we use our formule to calculate the slope of W-Z:

[tex]\frac{6-(-2)}{-1-(-2)}[/tex]  =  [tex]\frac{8}{1}[/tex]  =  8

if we use our formule to calculate the slope of X-Y:

[tex]\frac{8-0}{2-1}[/tex]  =  [tex]\frac{8}{1}[/tex]  =  8

  • We know that parallel lines will never intersect because they have the same slope, therefore W-Z side is parallel to X-Y side

2. Then we have the W-X side that it's supossed to be parallel to Z-Y side

if we use our formule to calculate the slope of W-X:

[tex]\frac{6-8}{-1-2}[/tex]  =  [tex]\frac{-2}{-3}[/tex]  

if we use our formule to calculate the slope of Z-Y:

[tex]\frac{-2-0}{-2-1}[/tex]  =  [tex]\frac{-2}{-3}[/tex]  

  • We know that parallel lines will never intersect because they have the same slope, therefore W-X side is parallel to Z-Y side

Then we have to prove that the parallalel sides are equal length to each other.

The formule we use to get the distance between two points is:

[tex]\sqrt{(x2-x1)^{2}+(y2-y1)^{2} }[/tex]

We calculate the lenght of the W-Z side that it's supossed to be equal to X-Y side:

W-Z = [tex]\sqrt{(-1-(-2))^{2}+(6-(-2))^{2} }[/tex] =   [tex]\sqrt{65}[/tex]

X-Y = [tex]\sqrt{(2-1)^{2}+(8-0)^{2} }[/tex] = [tex]\sqrt{65}[/tex]

So the W-Z side have the same lenght to X-Y side.

We calculate the lenght of the W-X side that it's supossed to be equal to Z-Y side:

W-X = [tex]\sqrt{(-1-2)^{2}+(6-8)^{2} }[/tex] =   [tex]\sqrt{13}[/tex]

Z-Y = [tex]\sqrt{(-2-1)^{2}+(-2-0)^{2} }[/tex] = [tex]\sqrt{13}[/tex]

So the W-X side have the same lenght to Z-Y side.

akposevictor

Quadrilateral WXYZ have two pairs of equal sides that are parallel, it is a parallelogram.

Properties of a Parallelogram

  • When two sides of a quadrilateral are parallel, their slopes will be equal, therefore, the opposite sides of a parallel must be equal and also have the same slope.
  • Distance formula for calculating the distance between two points is given as, [tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex].
  • Slope = change in y / change in x

Given:

W(−1,6)

X(2, 8)

Y(1, 0)

Z(−2,−2)

Find the slope of WX and YZ:

Slope of WX = (8 - 6)/(2 - (-1)) = 2/3

Slope of YZ = (-2 - 0)/(-2 - 1) = -2/-3 = 2/3

Find the slope of XY and WZ:

Slope of XY = (8 - 0)/(2 - 1) = 8

Slope of WZ = (-2 - 6)/(-2 -(-1)) = 8

Since the each pair of opposite sides of quadrilateral WXYZ  have the same slope, therefore, the opposite sides are parallel to each other.

Thus, applying the distance formula, [tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex], the opposite side lengths are:

XY = WZ = √65

WX = YZ = √13.

Therefore, quadrilateral WXYZ have two pairs of equal sides that are parallel, it is a parallelogram.

Learn more about parallelogram on:

https://brainly.com/question/12167853

Otras preguntas