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 

`((-5 + 1)/2, (6 + 4)/2) = (-2, 5)`

Slope of BD = `(4 - 6)/(1 + 5) = (-2)/6 = (-1)/3`

For line BD:

Slope = m = `(-1)/3`, (x₁, y₁) = (–5, 6)

Equation of the line BD is

y – y₁ = m(x – x₁)

`y - 6 =(-1)/3 (x + 5)`

3y – 18 = –x – 5

x + 3y = 13

For line AC:

Slope = m `(-1)/"slope of BD"` = 3, (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