# If the coordinates of the mid-points of the sides of a triangle are (3, 4), (4, 6) and (5, 7), find its vertices

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If the coordinates of the mid-points of the sides of a triangle are (3, 4), (4, 6) and (5, 7), find its vertices.

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Let A(x1,y1), B(x2,y2), C(x3,y3) be the vertices of ΔABC

Let D(3, 4), E(4, 6) and F(5, 7) be the midpoints of BC, CA and AB.

Since, D is the midpoint of BC

From (iii) and (iv)

Hence the vertices of triangle ABC are (6,9);(4,5);(2,3)