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

KnowledgeBoat · Accepted Answer

The rhombus ABCD is shown in the figure below: By formula, Slope = Substituting values we get, Equation of BD by point-slope form, ⇒ y - y₁ = m(x - x₁) ⇒ y - 6 = [x - (-5)] ⇒ 3(y - 6) = -1(x + 5) ⇒ 3y - 18 = -x - 5 ⇒ 3y + x - 18 + 5 = 0 ⇒ x + 3y - 13 = 0 ⇒ x + 3y = 13. Since, diagonals of rhombus are perpendicular to each other. So, product of their slopes will be -1. Slope of AC × Slope of BD = -1 = -1 Slope of AC = -1 × -3 = 3. We know that, Diagonals of rhombus bisect each other. Let diagonals meet at point O. ∴ Mid-point of AC = Mid-point of BD. Co-ordinates of mid-point of BD (i.e. O) = = (-2, 5). ∴ Co-ordinates of mid-point of AC = (-2, 5). Equation of AC by point-slope form, ⇒ y - y₁ = m(x - x₁) ⇒ y - 5 = 3[x - (-2)] ⇒ y - 5 = 3[x + 2] ⇒ y - 5 = 3x + 6 ⇒ 3x - y + 6 + 5 = 0 ⇒ 3x - y + 11 = 0 ⇒ y = 3x + 11. Hence, equation of BD is x + 3y = 13 and equation of AC is y = 3x + 11.

Mathematics

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

Straight Line Eq

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Mathematics

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

Straight Line Eq

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