If a vertex of a triangle be (1, 1) and the middle points of the sides through it be (-2, 3) and (5, 2), find the other vertices.
Let in ∆ABC, A(1,1), B(x1, y1) and C(x2, y2).
Let D(-2, 3) and E(5, 2) be the midpoints of sides AB and AC respectively.
By midpoint formula.
x = , y =
For mid point D (-2, 3) of side AB,
-2 = , 3 =
1 + x1 = -4 and 1 + y1 = 6
x1 = -5 and y1 = 5
∴ B ( x1, y1) ≡ (-5, 5)
For midpoint E(5, 2) of side AC,
5 = , 2 =
1 + x2 = 10 and = 4
∴ x2 = 9 and = 3
∴ C(x2, y2) ≡ (9, 3)
Hence other two vertices are B (-5, 5) and C(9, 3)