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

The coordinates of P, the point of intersection of diagonals CE and DH in parallelogram CDEH, are P(-3, 2), calculated using the midpoint formula on the end vertices of both diagonals.

Step-by-step explanation:

The point P, the point of intersection of diagonals CE and DH of a parallelogram CDEH, can be found using the midpoint formula, since diagonals of a parallelogram bisect each other. The midpoint M of a line segment with endpoints (x1, y1) and (x2, y2) is given by M = ((x1 + x2) / 2, (y1 + y2) / 2). Applying this to diagonals CE and DH with given vertices C(-5, 5), D(2, 5), E(-1, -1), and H(-8, -1), we can find the coordinates of P.

First, find the midpoint of diagonal CE with vertices C(-5, 5) and E(-1, -1):
M1 = ((-5 + (-1)) / 2, (5 + (-1)) / 2) = (-6 / 2, 4 / 2) = (-3, 2).

Then, find the midpoint of diagonal DH with vertices D(2, 5) and H(-8, -1):
M2 = ((2 + (-8)) / 2, (5 + (-1)) / 2) = (-6 / 2, 4 / 2) = (-3, 2).

Both midpoints M1 and M2 are the same, so the coordinates of P, the intersection point of diagonals CE and DH, are P(-3, 2).

Answer 2

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((x_1+x_2)/(2),(y_1+y_2)/(2)\right)`

`P=\left((-5+(-1))/(2),(5+(-1))/(2)\right)`

`P=\left((-5-1)/(2),(5-1)/(2)\right)`

`P=\left((-6)/(2),(4)/(2)\right)`

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

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