Diagonal of a square from 4 points

mhester88

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I'm very lost on this word problem and have no idea what to do here. Is there anyone who understands this and may be able to help?

A diagonal of a square connects the points (-4,3) and (2,-3). Find the area and the perimeter of the square.​
 
Draw a picture!
Find the length of the diagonal. Then use the Pythagorean theorem to find the length of the sides
 
I really appreciate your reponse, that was really fast! I still don't quite understand what I am supposed to do with the points or how to find a diagonal though :/
 
I'm very lost on this word problem and have no idea what to do here. Is there anyone who understands this and may be able to help? A diagonal of a square connects the points (-4,3) and (2,-3). Find the area and the perimeter of the square.
If the points \((-4,3)~\&~(2,-3) \) are endpoints of a diagonal of a square.
Then the points \((-4,-3)~\&~(2,3)\) are the other vertices. Do you see why?
 
Thank you for the detailed response. If I understand this correctly and graph out the square, then each side equals 6. This would also mean that a=36 and p=24. Does it sound like I have this right?
 
mhester88 said:
If I understand this correctly and graph out the square, then each side equals 6.
This would also mean that a=36 and p=24. Does it sound like I have this right?


The area is 36 square units and the perimeter is 24 units.

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Here is another approach, or consider it a way to check instead.

If d = the length of a diagonal of a square, then the number of
square units in that square's area equals \(\displaystyle \ 0.5d^2. \ \ \)

In this case, \(\displaystyle \ 0.5d^2 \ = \ 0.5[(-4 - 2)^2 + (3 - (-3))^2] \ = \)

\(\displaystyle 0.5[(-6)^2 + (6)^2] \ =\)

\(\displaystyle 0.5(36 + 36) \ = \)

\(\displaystyle 0.5(72) \ = \)

\(\displaystyle 36\)



This formula goes directly into squaring the length of a diagonal
of a square and then multiplying that by 0.5.
 
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