Question

find the coordinates of the intersection of the diagonals of parallelogram PQRS with vertical P(-5,5) Q(2,5) , R(4,-3) and S(-3,-3)

Answer 1

Given:

The vertices of parallelogram PQRS are P(-5,5) Q(2,5) , R(4,-3) and S(-3,-3).

To find:

The intersection of the diagonals of parallelogram PQRS.

Solution:

We know that the diagonals of a parallelogram bisect each other.

In parallelogram PQRS, PR and QS are the diagonals of the parallelogram.

It means the intersection of PR and QS is the midpoint of PR and QS.

Midpoint formula:

$Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)$

Midpoint of diagonal PR is:

$Midpoint=\left(\dfrac{(-5)+4}{2},\dfrac{5+(-3)}{2}\right)$

$Midpoint=\left(\dfrac{-1}{2},\dfrac{2}{2}\right)$

$Midpoint=\left(-0.5,1\right)$

Therefore, the coordinates of the intersection of the diagonals of parallelogram PQRS are (-0.5,1).