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On a Cartesian coordinate plane, points (1,2)  and (7,4) are opposite vertices of a square. What is the area of the square?

 

thanks!

 Feb 11, 2019

Best Answer 

 #1
avatar+17269 
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I will assume that  'opposite vertices' means diagonal corners.....

 

Find the length of the diagonal

 

Diagonal^2 = (1-7)^2 + (2-4)^2

                   = 36 + 4

                    = 40

Diagonal = sqrt 40       

 

It is a square, so the side lengths are all the same....the diagonal makes a right triangle with the sides

s^2 + s^2 = 40 ^2

2s^2=40^2

s^2 = 40^2 / 2

s^2 = 800

s= 28.28   units        Area = s x s = s^2 = 800 units^2        

 Feb 11, 2019
 #1
avatar+17269 
+2
Best Answer

I will assume that  'opposite vertices' means diagonal corners.....

 

Find the length of the diagonal

 

Diagonal^2 = (1-7)^2 + (2-4)^2

                   = 36 + 4

                    = 40

Diagonal = sqrt 40       

 

It is a square, so the side lengths are all the same....the diagonal makes a right triangle with the sides

s^2 + s^2 = 40 ^2

2s^2=40^2

s^2 = 40^2 / 2

s^2 = 800

s= 28.28   units        Area = s x s = s^2 = 800 units^2        

ElectricPavlov Feb 11, 2019

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