Question

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

@Sheraz12345 @Hero @ganeshie8 ?

Answer 2

@Sheraz12345 ?

Answer 3

@ganeshie8 ! Can you help me please?

Answer 4

how can we show that two lines are perpendicular ?

Answer 5

I don't know

Answer 6

know how to find slope, given two points ?

Answer 7

y1-y2/x1-x2?

Answer 8

Awesome ! thats all we need for doing this problem :)

Answer 9

Really?

Answer 10

use below :
two lines are perpendicular if the product of slopes equals -1

Answer 11

Okay, and that's it!?

Answer 12

1) find the slope of each diagonal segment
2) show that the product equals -1

Answer 13

Okay, let me do this

Answer 14

given vertices :
A(-5, -1), B(-9, 6), C(-1, 5), and D(3, -2)

Answer 15

slope of diagonal AC = ?
slope of diagonal BD = ?

Answer 16

I got -4/7 for AB

Answer 17

Oh wait, let me do AC

Answer 18

-4/-6

Answer 19

Is that right @ganeshie8 ?

Answer 20

careful, you need to put `y coordinates` in the numerator

Answer 21

its y1-y2 / x1 - x2

NOT x1-x2 / y1-y2

Answer 22

Oh, okay wait

Answer 23

-6/-4?

Answer 24

and we just need to find two slopes : AC and BD

Answer 25

-6/-4 for what ?

Answer 26

AC

Answer 27

correct ! you may simplify it...

Answer 28

-3/-1

Answer 29

3

Answer 30

nope, try again

Answer 31

Wups, -3/-2

Answer 32

Yes !

Answer 33

So, slope of AC = 3/2

Answer 34

find the slope of BD also

Answer 35

Does that simplify to 3/2?

Answer 36

Ohm, okay

Answer 37

Okay, let me find BD

Answer 38

8/-12

Answer 39

So 2/-3?

Answer 40

or -2/3

Answer 41

Okay

Answer 42

slope of BD = -2/3

Answer 43

multiply both the slopes, what do u get ?

Answer 44

You get -1!

Answer 45

Excellent !! Since hte product of slopes of diagonals is -1, the diagonals AC and BD are perpendicular.

Answer 46

So it is a parallelogram

Answer 47

It is a parallelogram already.

Answer 48

Oh, I must of misunderstood what they where asking me to prove.

Answer 49

we have just proven that the given parallelogram is a `rhombus` also

Answer 50

its both a parallelogram and a rhombus !

Answer 51

Okay, yeah that makes sense.

Answer 52

Thank you @ganeshie8 !

Answer 53

np :)