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!
+36915 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
+36915 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
