Question

A = (7, -2) and C = (-1, -6) are the vertices of square ABCD. Find the equations of diagonals AC and BD.

Answer 1

We know that in a square, diagonals bisect each other at right angle.

Let O be the point of intersection of the diagonals AC and BD.

Co-ordinates of O are

Slope of AC =

For line AC:

Slope = m = , (x₁, y₁) = (7, -2)

Equation of the line AC is

y - y₁ = m(x - x₁)

y + 2 = (x - 7)

2y + 4 = x - 7

2y = x - 11

For line BD:

Slope = m = , (x₁, y₁) = (3, -4)

Equation of the line BD is

y - y₁ = m(x - x₁)

y + 4 = -2(x - 3)

y + 4 = -2x + 6

2x + y = 2