2. A parallelogram has the vertices (-1, 2), (4, 4), (2, -1) and (-3, -3). Determine what type of parallelogram [10 points]. Find the perimeter and area [20 points].

- anonymous

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- anonymous

##### 1 Attachment

- anonymous

That's what I got...but clearly it's not a parallelogram, so what am I doing wrong, and what do I need to do differently?

- anonymous

@ganeshie8, please help!

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## More answers

- ganeshie8

http://prntscr.com/3eu6hv

- ganeshie8

^^thats how it should look.
graphing is a very good idea, but u dont need to graph to solve this problem.

- anonymous

Ohhh...duh.
Apparently I'm going to be stupid today, brilliant. Thnx for the help! :)

- ganeshie8

u figured how to work the problem ?

- anonymous

BTW, someone told me the answer to this problem was 12. Are they right? I got 4.2...
√((3) – (0))² + ((0) – (3))² = √3² + -3² = √9 + 9 = √18 ≈ 4.2

- anonymous

yes, I did

- ganeshie8

show me ur complete work

- anonymous

For the first problem?

- ganeshie8

for both

- anonymous

Ah...ok

- ganeshie8

what ever u have so far...

- anonymous

just a mo, then

- anonymous

##### 1 Attachment

- anonymous

working on the second question now

- ganeshie8

Are you given instructions that u need to work it by graphing ?

- anonymous

Yeah, they taught graphing and the distance formula and whatnot

- ganeshie8

no, i mean did the instructions specifically ask u to do this by graphing ?

- ganeshie8

cuz, u should NOT use graphing unless the instructions say so

- ganeshie8

the common/regular way to work this problem is by finding lengths of sides using `distance formula` and the slopes of sides using `slope formula`

- anonymous

http://static.k12.com/eli/bb/343/-1/0/1_124724_23955/-1/0c7f4350276a46b214395670eae2d3ec752620d8/media/e3eb7b41ab24f0e612428cb2ca67db83e139e1b7/83879.PDF

- anonymous

Those were the directions they gave me

- ganeshie8

cool :) then you're right ! they want u work it by graphing

- anonymous

Given that they gave me the graph, I would assume that they want me to solve it by graphing, but I also used the distance formula to find the lengths of the sides

- anonymous

ok :)

- ganeshie8

good :)
your length of sides, and perimeter are correct.
but Area is wrong.

- ganeshie8

squaring sides will not give u Area for a rhombus.

- anonymous

ohh..just looked it up A - diagonal x diagonal/2

- ganeshie8

Area of rhombus = \(\frac{1}{2} d_1 d_2\)

- ganeshie8

yes^

- anonymous

Great, now I have to find the diagonals, lol

- ganeshie8

its easy from graph

- ganeshie8

horizontal diagonal = 3--3 = 6
vertical diagonal = 3--3 = 6

- ganeshie8

So, Area = \(\frac{1}{2} d_1 d_2 = \frac{1}{2} 6*6 = 18\)

- ganeshie8

And that makes the given rhombus a SQUARE !

- ganeshie8

so the given parallelogram is not just a rhombus, its also a SQUARE !

- ganeshie8

for the `type of parallelogram `, you should say that its a `square`

- ganeshie8

if that makes any sense..

- anonymous

The parallelogram is a rhombus and a square?

- ganeshie8

just say its a SQUARE !

- anonymous

rhomus: all equal sides, two pairs of equal angles
square: equal sides, equal angles

- anonymous

oh, ok

- anonymous

Does that change my equation for the area, then?

- ganeshie8

all squares are parallelograms
all squares are rhombuses
all squares are rectangles
all squares are quadrilaterals

- ganeshie8

a square is many things

- ganeshie8

yes it will change ur formula, but the answer will be same

- anonymous

I see that, lol

- ganeshie8

let me modify it and give u

- anonymous

it will be?

- anonymous

ok

- ganeshie8

here is the corrected stuff for question 1 :
http://prntscr.com/3euc4h

- anonymous

##### 1 Attachment

- anonymous

how do you find the diagonals inside a rhombus?

- ganeshie8

use the distance formula

- anonymous

oh, its the same process, ok, hold on

- ganeshie8

ok, i presume u knw what a diagonal is :)

- ganeshie8

it just connects the opposite vertices

- ganeshie8

|dw:1398867292759:dw|

- ganeshie8

|dw:1398867314860:dw|

- ganeshie8

^^those two line segments joining opposite vertices are diagonals

- anonymous

##### 1 Attachment

- anonymous

Is that correct? I found it odd that I got the same area for #1 and #2...but maybe that's just a coincidence

- ganeshie8

diagonals are not equal in rhombus

- ganeshie8

so u need to calculate the 2nd diagonal also using distance formula

- ganeshie8

and then use the area of rhombus formula :
Area = \(\frac{1}{2}d_1 d_2\)

- anonymous

##### 1 Attachment

- anonymous

@ganeshie8

- ganeshie8

looks good !

- anonymous

thnx! :D

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