Question

B (-5, 6) and D (1, 4) are the vertices of rhombus ABCD. Find the equations of diagonals BD and AC.

Answer 1

We know that in a rhombus, 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 BD =

For line BD:

Slope = m = , (x₁, y₁) = (-5, 6)

Equation of the line BD is

y - y₁ = m(x - x₁)

y - 6 = (x + 5)

3y - 18 = -x - 5

x + 3y = 13

For line AC:

Slope = m = , (x₁, y₁) = (-2, 5)

Equation of the line AC is

y - y₁ = m(x - x₁)

y - 5 = 3(x + 2)

y - 5 = 3x + 6

y = 3x + 11