Question

The mid-points D, E, F of the sides of a triangle ABC are (3, 4), (8, 9) and (6, 7). Find the coordinates of the vertices of the triangle

Answer 1

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

So, x1 + x2 = 3...(1)
y1 + y2 = 4...(2)
x2 + x3 = 8...(3)
y2 + y3 = 9...(4)
x1 + x3 = 6...(5)
y1 + y3 = 7...(6)

Adding (1), (3) and (5),
2(x1+x2+x3) = 17
or, x1 + x2 + x3 = 8.5 ...(7)
Subtracting (1), (3) and (5) from (7),
x3 = 5.5, x1 = 0.5, x2 = 2.5

Adding (2), (4) and (6),
2(y1+y2+y3) = 20
or, y1 + y2 + y3 = 10 ...(8)
Subtracting (1), (3) and (5) from (8),
y3 = 6, y1 = 1, y2 = 3

Answer:- Co ordinates of the vertices of the triangle are A(0.5,1), B(2.5,3) and C(5.5,6)