Question

If the coordinates of two opposite vertices of a square are (6,-3) and (-2,3)
then the area of square

Answer 1

Answer:

area = 50

Step-by-step explanation:

If a square has side length s, then by Pythagoras' Theorem, the length of the diagonal is

d = √(s²+s²) = √(2s²) = s√2.

So if we know the diagonal d, then we can get the side length:

s = d / √2.

As (6, -3) and (-2, 3) are opposite vertices of a square, the diagonal of the square is the distance between these points:

d = √( ( 6 - -2 )² + ( -3 - 3 )² )  = √( 8²+ 6² ) = √( 64 + 36 ) = √100 = 10

So the side length is

s = 10 / √2

and the area is then

area = s² = ( 10/√2 )² = 100 / 2 = 50