Question

Use the diagonals to tell whether a parallelogram with the given vertices is a rectangle, rhombus, or square. Give all names that apply.

Q(-8,-2) T(-6,8) W(4,6) Z(2,-4)

Answer 1

Search up images of graph paper then try graphing these @Seratul

Answer 2

I am not allowed to graph them. It would be too easy that way o.O

Answer 3

Can you guess from this graph?

Answer 4

Square and rectangle?

Answer 5

I think you have square but look at this one and see. Im not to sure.. Im only good at graphing points XD

Answer 6

Then I don't think you can help me xD. I need to make sure it is a certain shape with diagonals.

Answer 7

Eh well i tried XD Sowwie

Answer 8

Here are some points regarding diagonals of each of the mentioned figures:

1. Rectangle -> Diagonals are equal and bisect each other but not perpendicularly
2. Rhombus -> Diagonals are perpendicular bisectors of each other but not equal
3. Square -> Diagonals equal and perpendicular bisectors of each other
4. Parallelogram -> Diagonals bisect each other.. no need to be equal

Answer 9

Any doubt with this?

Answer 10

I'm pretty sure the diagonals of rectangles bisect each other perpendicularly.

Answer 11

Anyways, I still think it would be a square and rectangle.

Answer 12

A rhombus is a rectangle with all sides equal or diagonals perpendicular bisecting each other

Answer 13

So all three?

Answer 14

Q(-8,-2) T(-6,8) W(4,6) Z(2,-4)

What is the order of the vertices ?

Answer 15

I mean the figures should be QTWZ or QWTZ or anything else?

Answer 16

I think the basic shape is what the previous person drew above.

Answer 17

Lite.. it is QTWZ...

Answer 18

So anyways... start by calculating the slope of QW and TZ

Answer 19

Can you do this?

Answer 20

Yea.
QW: 6--2/4--8 = 8/12 = 2/3
TZ: -4-8/2--6 = -12/8= -3/2
They are negative reciprocals so they are parallel.

Answer 21

But we know that since they are parallelograms which is given.

Answer 22

Naah naah!! Because the slopes are negative reciprocals they are perpendicular... for parallel the slopes must be the same

Answer 23

Whoops, my bad xD.

Answer 24

Thus, diagonals QW and TZ are perpendicular.. thus, it can either be a square of a rhombus.. now you just need to see whether diagonals are equal or not

Answer 25

Use the distance formula for finding the length of QW and TZ

Answer 26

Why can't it be a rectangle?

Answer 27

Oh wait, the diagonals aren't perpendicular.

Answer 28

Because for a rectangle the diagonals are not perpendicular to each other...

Answer 29

Okay, so know we use midpoint formula?

Answer 30

No.. we use distance formula

Answer 31

We want to find out the length of QW and TZ

Answer 32

QW: (4--8)^2 + (6--2)^2 = 12^2 + 8^2 = 144 +64 = sqrt 208 = 4 radical 13

Answer 33

TZ: (2--6)^2 + (-4-8)^2 = 8^2 + -12^2 = 64 + 144 + sqrt 208 = 4 radical 13

Answer 34

Okay, they are the same length.

Answer 35

Great!

Answer 36

So the figure is a square

Answer 37

Okay, i'm going to have to memorize the properties of the parallelograms. Thank you very much!

Answer 38

:) Your welcome