Question

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

Answer 1

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

Let D(3, -2), E(-3, 1) and F(4, -3) be the midpoint of sides , BCCAand AB respectively

Since, D is the midpoint of BC

Similarly, E and F are the midpoint of CA and AB respectively.

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

So, the coordinates of A are (-2,0)

From (ii) and (iv)

So, the coordinates of B are (10,-6)

From (iii) and (iv)

So, the coordinates of C are (-4,2)

Hence, the vertices of ΔABC are A(-2,0), B(10,6) and C(-4,2)