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

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 (x 1 , y 1 ), B(x 2 , y 2 ), C(x 3 , y 3 ). 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, ∴ x 1 + x 2 + x 3 = 1. On subtracting Eq 3 from Eq 7 we get, x 1 + x 2 + x 3 - (x 2 + x 3 ) = 1 - 1 x 1 + x 2 + x 3 - x 2 - x 3 = 0 x 1 = 0. On subtracting Eq 5 from Eq 7 we get, x 1 + x 2 + x 3 - (x 3 + x 1 ) = 1 - 1 x 1 + x 2 + x 3 - x 3 - x 1 = 0 x 2 = 0. On subtracting Eq 1 from Eq 7 we get, x 1 + x 2 + x 3 - (x 1 + x 2 ) = 1 - 0 x 1 + x 2 + x 3 - x 1 - x 2 = 1 x 3 = 1. Adding Eq 2, 4 and 5, ∴ y 1 + y 2 + y 3 = 1. (Eq 8) On subtracting Eq 4 from Eq 8 we get, y 1 + y 2 + y 3 - (y 2 + y 3 ) = 1 - 1 y 1 + y 2 + y 3 - y 2 - y 3 = 0 y 1 = 0. On subtracting Eq 6 from Eq 8 we get, y 1 + y 2 + y 3 - (y 3 + y 1 ) = 1 - 0 y 1 + y 2 + y 3 - y 3 - y 1 = 1 y 2 = 1. On subtracting Eq 2 from Eq 8 we get, y 1 + y 2 + y 3 - (y 1 + y 2 ) = 1 - 1 y 1 + y 2 + y 3 - y 1 - y 2 = 1 - 1 y 3 = 0. Hence, coordinates of vertices of triangle are (0, 0), (0, 1) and (1, 0) respectively.

If two vertices of a parallelogram are (3, 2), (-1, 0) and its diagonals meet at (2, -5), find the other two vertices of the parallelogram.

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Show by section formula that the points (3, -2), (5, 2) and (8, 8) are collinear.

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Mathematics

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

Section Formula

Related Questions

If two vertices of a parallelogram are (3, 2), (-1, 0) and its diagonals meet at (2, -5), find the other two vertices of the parallelogram.

Find the third vertex of a triangle if its two vertices are (-1, 4) and (5, 2) and mid-point of one side is (0, 3).

Show by section formula that the points (3, -2), (5, 2) and (8, 8) are collinear.

Find the value of p for which the points (-5, 1), (1, p) and (4, -2) are collinear.