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.

Given: points ( - 2, - 1), (1, 0), (4, 3) and (1, 2)

To find: coordinates of point where diagonals meet.

Formula Used:

section formula:

If point P (x, y) divides the line segment A (x₁, y₁) and B(x₂,y₂)

Then the coordinates of P are:

Explanation:

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

We know that diagonals of a parallelogram bisect each other.

Hence, we find the midpoint of AC.

As mid - point divides a line into 1:1.

By section formula,

For point E (x, y)

∴ E (x_, y) = (1 , 1 )