Question

ing 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.

Answer 1

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 = $\frac{y-y1}{x-x1}$

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:

$\frac{6-(-2)}{-1-(-2)}$  =  $\frac{8}{1}$  =  8

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

$\frac{8-0}{2-1}$  =  $\frac{8}{1}$  =  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:

$\frac{6-8}{-1-2}$  =  $\frac{-2}{-3}$  

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

$\frac{-2-0}{-2-1}$  =  $\frac{-2}{-3}$  

• 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:

$\sqrt{(x2-x1)^{2}+(y2-y1)^{2} }$

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

W-Z = $\sqrt{(-1-(-2))^{2}+(6-(-2))^{2} }$ =   $\sqrt{65}$

X-Y = $\sqrt{(2-1)^{2}+(8-0)^{2} }$ = $\sqrt{65}$

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 = $\sqrt{(-1-2)^{2}+(6-8)^{2} }$ =   $\sqrt{13}$

Z-Y = $\sqrt{(-2-1)^{2}+(-2-0)^{2} }$ = $\sqrt{13}$

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