# If the coordinates of the mid-points of the sides of a triangle are (1, 1), (2, —3) and (3, 4), find the vertices of the triangle.

153 views

If the coordinates of the mid-points of the sides of a triangle are (1, 1), (2, -3) and (3, 4), find the vertices of the triangle.

by (13.1k points)
selected

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

Let D(1, 1), E(2, -3) and F(3, 4) be the mid-points of sides BC, CA and AB respectively.

Since, D is the mid-point of  BC.

Similarly E and F are the mid-points of CA and AB respectively.

From (i), (ii) and (iii) we get

From (i) and (iv) we get

So the coordinates of A are (4,0)

From (ii) and (iv) we get

So the coordinates of B are (2,8)

From (iii) and (iv) we get

So the coordinates of C are (0,-6)

Hence, the vertices of triangle ABC are:

A(4,0), B(2,8) and C(0,-6)