Question

The coordinate of the vertices of parallelogram CDEH are C(-5,5), D(2,5), E(-1,-1), and H(-8,-1). What are the coordinates of P, the point of intersection of diagonals CE and DH?

Answer 1

Given:

Vertices of a parallelogram are C(-5,5), D(2,5), E(-1,-1), and H(-8,-1).

P is the intersection point of diagonals CE and DH.

To find:

The coordinates of P.

Solution:

We know that, diagonals of a parallelogram always bisect each other. It means the intersection point of the diagonal is the midpoint point of both diagonals.

We can find the midpoint of either diagonal CE or diagonal DH to get the coordinates of intersection point of diagonals, i.e. P.

So, point P is midpoint of CE. So,

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

$P=\left(\dfrac{-5+(-1)}{2},\dfrac{5+(-1)}{2}\right)$

$P=\left(\dfrac{-5-1}{2},\dfrac{5-1}{2}\right)$

$P=\left(\dfrac{-6}{2},\dfrac{4}{2}\right)$

$P=\left(-3,2\right)$

Therefore, the coordinates of point P are (-3,2).