Question

**PLEASE HELP**

Verify that parallelogram ABCD with vertices A(-5, -1), B(-9, 6), C(-1,5), and D(3,-2) is a rhombus by showing that it is a parallelogram with perpendicular diagonals.

Answer 1

@jim_thompson5910

Answer 2

use distamce formula sqrt((x1-x2)^2+(y1-y2)^2) to count the dstance. The wrte eqaution of diagonals and verify thats their slopes are negative reciprocals

Answer 3

You need to show that the slope of the line AC multiplied by the slope of the line BD is equal to -1

Answer 4

two lines are perpendicular if the product of their slopes equals -1

Answer 5

Okay... So now im more confused...

Answer 6

A(-5, -1), C(-1,5)

what is the slope of the line through A and C

Answer 7

use the slope formula
\[\Large m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\]

Answer 8

4, -6?? @jim_thompson5910

Answer 9

Slope of the line through point A and point C
\[\Large m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\]
\[\Large m = \frac{5-(-1)}{-1-(-5)}\]
\[\Large m = \frac{5+1}{-1+5}\]
\[\Large m = \frac{6}{4}\]
\[\Large m = \frac{3}{2}\]

Answer 10

I made (x1,y1) be point A (-5,-1)

I made (x2,y2) be point B (-1,5)

Answer 11

hopefully it makes sense?

Answer 12

So what do i say for the answer?
(x1,y1) be point A (-5,-1)

(x2,y2) be point B (-1,5) ???

Answer 13

@jim_thompson5910

Answer 14

we want to find the slope of line AC

that's why I made A the point (x1,y1)
and C the point (x2,y2)

Answer 15

I'm not dealing with point B right now

Answer 16

AC is one diagonal
BD is the other diagonal (we'll focus on that later)

Answer 17

Okay.. So what are we focusing on right now?

Answer 18

finding the slope of AC

Answer 19

I want to make sure you understand

Answer 20

asnaseer has a good pic drawn above