Question

If A (6, 2) and C (-1, 3) are two opposite vertices of a square, find the equation of its sides

Answer 1

The diagonals are perpendicular and bisect each other, so
AC = -1/7 x + 20/7
These intersect at the midpoint M = (5/2, 5/2), so
BD = 7x - 15
The distance AB = √50 = 5√2
so the sides of ABCD have length 5
so, if D is at (h,k) then we need
√((h-6)^2 + (k-2)^2) = 5
so, since (h,k) lies on BD, that means
√((h-6)^2 + ((7h-15)-2)^2) = 5
h = 2 or 3, so k = -1 or 6
B = (2,-1) and D = (3,6)