The coordinates of the vertex A of a square ABCD is (1, 2) and the equation of diagonal BD is x + 2y = 10. Find the equation of the other diagonal and the co-ordinates of the centre of the square.
Straight Line Eq
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Question

The coordinates of the vertex A of a square ABCD is (1, 2) and the equation of diagonal BD is x + 2y = 10. Find the equation of the other diagonal and the co-ordinates of the centre of the square.

KnowledgeBoat · Accepted Answer

The square is shown in the fig below: Given, Equation of diagonal BD is x + 2y = 10 ⇒ 2y = -x + 10 ⇒ y = Comparing it with y = mx + c, we get : Slope (m₁) = . We know that, Diagonals of a square are perpendicular to each other and product of slopes of perpendicular lines = -1. Let slope of diagonal AC = m₂. By point-slope form, Equation of AC is y - y₁ = m(x - x₁) ⇒ y - 2 = 2(x - 1) ⇒ y - 2 = 2x - 2 ⇒ 2x - 2 + 2 = y ⇒ y = 2x. Since, center of the square is the point of intersection of its diagonals. Solving, x + 2y = 10 and y = 2x simultaneously, we get : ⇒ x + 2y = 10 .......(1) ⇒ y = 2x .........(2) Substituting value of y from eq (2) in (1), we get : ⇒ x + 2(2x) = 10 ⇒ x + 4x = 10 ⇒ 5x = 10 ⇒ x = ⇒ x = 2. ⇒ y = 2x = 2(2) = 4. Center = (2, 4). Hence, equation of other diagonal is y = 2x and coordinates of circle = (2, 4).

Mathematics

The coordinates of the vertex A of a square ABCD is (1, 2) and the equation of diagonal BD is x + 2y = 10. Find the equation of the other diagonal and the co-ordinates of the centre of the square.

Straight Line Eq

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