Question

Find the coordinates of the point where the diagonals of the parallelogram formed by joining the points (-2, -1), (1, 0), (4, 3) and (1, 2) meet.

Answer 1

Let our points of parallelogram be A(-2, -1), B(1, 0), C(4, 3) and D(1, 2) and mid point of diagonals be E(x,y)

We know that diagonals of parallelogram bisect each other. 

Hence, 

we find mid point of AC. 

By midpoint formula,

x = \(\frac{x_1 + x_2}2\), y = \(\frac{y_1 + y_2}2\)

For point E(x, y)

x₁ = \(\frac{-2 + 4}2\) , y₁ = \(\frac{-1 + 3}2\)

∴ x₁ = \(\frac{2 }2\) , y₁ = \(\frac{2 }2\)

∴ E (x, y) ≡ (1, 1 )