Plot points A(-3,2) B(4,2) C(2,-3) and D(-5,-3) Find its area and perimeter. PLS HELP ME

- anonymous

Plot points A(-3,2) B(4,2) C(2,-3) and D(-5,-3) Find its area and perimeter. PLS HELP ME

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- amistre64

i find it might make things simpler by "moving" this so that one of the points is at the origin; helps me to see the the shapes better

- anonymous

Plot the points according to your knowledge of coordinate system and then detect what figure is that whether it is square, rectangle or some other one.

- anonymous

Use distance formula for calculating side's distances

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## More answers

- anonymous

ITS A PARALLELOGRAM

- amistre64

since it feels to me that -5,-3 is the farthest away, ill adjust all the points by that
A(-3,2) B(4,2) C(2,-3) D(-5,-3)
5 3 5 3 5 3 5 3
------------------------------
2 5 9 5 7 0 0 0

- anonymous

If it is a parellelogram then use the formula for finding area of it :
base * corresponding height.

- anonymous

what is the base and height? pls help :(

- anonymous

Take any side as base and then decide the corresponding height. Wait lemme draw a diagram.

- amistre64

A(-3,2) B(4,2) C(2,-3) D(-5,-3)
5 3 5 3 5 3 5 3
------------------------------
2 5 9 5 7 0 0 0
^________^ ^-------^
5 high 7 wide

- anonymous

ok :) thanks for the hep :)

- amistre64

A(-3,2)
5 3
-----
2 5
^^^^ this is our offset, so that the slant length can be determined using pythag

- anonymous

|dw:1370436249151:dw||dw:1370436316532:dw|

- anonymous

thanks for all the help :)

- anonymous

(It depends what side you consider as base ) --- Amistre is explaining well. Follow him :)

- anonymous

uhm, I can't understand it very well, how can I find out the base and the height if there are coordinates?

- amistre64

2 5 9 5
0 0 7 0
a skewed rectangle retains the same area|dw:1370436472416:dw|

- amistre64

the base and height can be better seen by positioning this thing at the origin ... at least thats the simplest way i can see it

- amistre64

the corrdinants given correspond to:
2 5 9 5
||height is from 0 to 5
0 0 7 0
-------
base is from 0 to 7

- amistre64

bad formatted lol
2 5 /
/ the slanted side has a length of a 2,5 rt triangle
0 0 / to fiinsh with the perimete

- amistre64

we already have enough information for the area, can you tell me what you think it would be?

- anonymous

10? i really don't know im just in middle school :(

- amistre64

the area corresponds to the "rectangle" of the same proportions.
do you recall how to find the area of a rectangle?

- anonymous

W X H

- amistre64

correct, since the width is 7 and the hieght is 5 .... we can determine the area

- anonymous

35? :) but how did youu know that 7 is the width and 5 the height?

- anonymous

This will help .

##### 1 Attachment

- amistre64

it was easily determined after i "moved" it to the origin; all i needed to do was measure the height and width from the origin

- amistre64

|dw:1370437197893:dw|

- anonymous

I GET IT :) THANK YOU VERY MUCH :) BUT HOW ABOUT THE PERIMETER?

- anonymous

PFA

##### 1 Attachment

- anonymous

Add all the sides' distances to find the perimeter.

- amistre64

well, we already know 2 sides .. top and bottom are 7
we simply need to determine the slanted length

- amistre64

|dw:1370437317944:dw|

- amistre64

how do you find the length of that part of a rt triangle if you know the legs?

- amistre64

....kept trying to call it a hypothesis :) its the hypotenuse
thing pythag thrm

- anonymous

uhm, i'll try :)

- anonymous

29?

- amistre64

|dw:1370437515909:dw|

- amistre64

29 is part of it, but you have to sqrt it

- anonymous

it doesnt have a sqr rt

- amistre64

\[n^2 = 5^2 + 2^2\]
\[n^2 = 25 + 4\]
\[n^2 = 29\]
\[n = \sqrt{29}\]

- anonymous

ahhh :)

- anonymous

what will happen next?

- amistre64

and we have 2 of those parts giving us:\[7+7+\sqrt{29}+\sqrt{29}\]
\[14+2\sqrt{29}\]
as a perimeter, its up to you to determine of you want an exact result or an approximation

- anonymous

what is the exact result o.O?

- amistre64

that IS the exact result ... an approximation would have a single decimal expansion as a value.

- amistre64

sqrt(29) is approximately 5.4
14 + 2(5.4)
14 + 10.8 = 24.8 as an approximation

- anonymous

THANK YOU VERY MUCH <3 can you please help me with this problem? Plot the points M(-2,5) N(4,5) 0(7,1) P (-5,1) A.Find its area and perimeter B. How long is the median xy of MNOP?

- amistre64

i cant at the moment, but post it as a new question to the left and someone is bound to help you out :) i have a paying job that i have to attend to at the moment.

- amistre64

but as a hint, i see the -5 might be the lowest point, so id move it all and set P at the origin

- anonymous

oh sorry my bad :( but tanks for the help I really appreciate it :)

- amistre64

good luck

- anonymous

My solution :
You have four points :
A(-3,2) B(4,2) C(2,-3) and D(-5,-3)
\[\left.\begin{array}{c}A(-3,2)\\B(4,2)\\C(2,-3)\\D(-5,3)\end{array}\right ]\textbf{Given}\]
[Please check the attachment - Faye1 for the graph of these points ]
Calculate AB, BC , CD and AD (4 sides of the quadrilateral ABCD )
(Formula used : Distance Formula \(\rightarrow\) :
Distance between any two points : \(\large{(x_1,y_1)}\) and \(\large{(x_2,y_2)}\) is
\[\large{\sqrt{(x_2 - x_1 )^2 + (y_2 - y_1)^2 } } \]
So using this formula for calculating AB, BC , CD and AD :
AB : \(\large{\sqrt{7^2 + 0^2 } = \sqrt{7^2} = 7}\)
BC : \(\large{\sqrt{(2-4)^2 + (-3-2)^2 } = \sqrt{(-2)^2 + (-5)^2} = \sqrt{4 + 25} = \sqrt{29} }\)
CD : \(\large{\sqrt{(-5-2)^2 + (-3 + 3)^2 } = \sqrt{(-7)^2 + 0^2} = \sqrt{(-7)^2} = 7 }\)
AD : \(\large{\sqrt{(-5+3)^2 + (-3 -2 )^2 } = \sqrt{(4 + 25) } = \sqrt{29} }\)
So , it is clear that , BC = AD and AB = CD that is opposite sides are equal of the quadrilateral ABCD.
Thus, first of all, ABCD is a parallelogram .
Now, area of the parallelogram = base * corresponding height
Base (let us say that it is CD) and Corresponding height will be : (Say it is AM )
CD = \(7\) [Found above]
The coordinates of A is : (-3,2)
The coordinates of M is : (-3,-3)
AM = \(\sqrt{(0)^2 + (5)^2 } = \sqrt{25} = 5\)
Therefore area = CD * AM = 7 * 5 = 35 sq. unit
For perimeter:
AB + BC + CD + AD = \(7 + \sqrt{29} + 7 + \sqrt{29} \) = \(14 + 2\sqrt{29} \)

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