Diagonal of a square from 4 points

[mhester88]

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.​

 

[Steven G]

Draw a picture!
Find the length of the diagonal. Then use the Pythagorean theorem to find the length of the sides

 

[mhester88]

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 :/

 

[pka]

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?

 

[mhester88]

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?

 

[lookagain]

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.