Find the coordinates of the vertices of the triangle, the middle points of whose sides are .

Question

KnowledgeBoat · Accepted Answer

Let ABC be a triangle in which D, E and F are the mid-points of sides AB, BC and CA respectively. Let coordinates of A be (x₁, y₁), B(x₂, y₂), C(x₃, y₃). Applying mid-point formula on side AB, Applying mid-point formula on side BC, Applying mid-point formula on side CA, Adding Eq 1, 3 and 5, ∴ x₁ + x₂ + x₃ = 1. On subtracting Eq 3 from Eq 7 we get, x₁ + x₂ + x₃ - (x₂ + x₃) = 1 - 1 x₁ + x₂ + x₃ - x₂ - x₃ = 0 x₁ = 0. On subtracting Eq 5 from Eq 7 we get, x₁ + x₂ + x₃ - (x₃ + x₁) = 1 - 1 x₁ + x₂ + x₃ - x₃ - x₁ = 0 x₂ = 0. On subtracting Eq 1 from Eq 7 we get, x₁ + x₂ + x₃ - (x₁ + x₂) = 1 - 0 x₁ + x₂ + x₃ - x₁ - x₂ = 1 x₃ = 1. Adding Eq 2, 4 and 5, ∴ y₁ + y₂ + y₃ = 1. (Eq 8) On subtracting Eq 4 from Eq 8 we get, y₁ + y₂ + y₃ - (y₂ + y₃) = 1 - 1 y₁ + y₂ + y₃ - y₂ - y₃ = 0 y₁ = 0. On subtracting Eq 6 from Eq 8 we get, y₁ + y₂ + y₃ - (y₃ + y₁) = 1 - 0 y₁ + y₂ + y₃ - y₃ - y₁ = 1 y₂ = 1. On subtracting Eq 2 from Eq 8 we get, y₁ + y₂ + y₃ - (y₁ + y₂) = 1 - 1 y₁ + y₂ + y₃ - y₁ - y₂ = 1 - 1 y₃ = 0. Hence, coordinates of vertices of triangle are (0, 0), (0, 1) and (1, 0) respectively.

Mathematics

Find the coordinates of the vertices of the triangle, the middle points of whose sides are .

Section Formula

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