Question

ABCD is a square. The cooordinates of B and D are (-3, 7) and (5, -1) respectively. Find the equation of AC.

Answer 1

Slope of BD = `(7 + 1)/(-3 -5)` = 1

Slope of AC = 1

Mid point of AC = mid point of BD

O(x,y) = `((5 - 3)/2 , (-1 + 7)/2)` = (1,3)

Equation of AC ⇒ `("y" - "y"_1)/("x" - "x"_1)` = slope

⇒ `("y" - 3)/("x" - 1) = 1`

⇒ x - 1 = y - 3

⇒ x - y + 2 = 0

⇒ y = x + 2