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Question

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


Solution

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

open parentheses fraction numerator negative 5 plus 1 over denominator 2 end fraction comma fraction numerator 6 plus 4 over denominator 2 end fraction close parentheses equals open parentheses negative 2 comma 5 close parentheses

Slope of BD = fraction numerator 4 minus 6 over denominator 1 plus 5 end fraction equals fraction numerator negative 1 over denominator 3 end fraction

For line BD:

Slope = m = fraction numerator negative 1 over denominator 3 end fraction, (x1, y1) = (-5, 6)

Equation of the line BD is

y - y1 = m(x - x1)

y - 6 = fraction numerator negative 1 over denominator 3 end fraction (x + 5)

3y - 18 = -x - 5

x + 3y = 13

For line AC:

Slope = m = fraction numerator negative 1 over denominator s l o p e space o f space B D end fraction equals 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


Mathematics
Concise Mathematics
Standard X

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