If two vertices of a parallelogram are (3, 2), (-1, 0) and the diagonals cut at (2, -5), find the other vertices of the parallelogram.

Question

Philoid · Accepted Answer

Let the vertices be A(3, 2), B(-1, 0), C(x₁, y₁ ) and D(x₂, y₂ ).

Let diagonals cut at E(2, - 5).

We know that mid points of diagonals of parallelogram coincide.

By midpoint formula.

x_m = , y_m =

For midpoint E of diagonal AC,

2 = , -5 =

∴x₁ = 1 and y₁ = -12

∴ coordinates of C are (1, -12)

For midpoint E of diagonal BD,

2 = , -5 =

∴ x₂ = 5 and y₂ = -10

∴ coordinates of D are (5, -10)