Question

The coordinates 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¯¯¯¯¯¯¯¯¯
?(2 points)
(
,
)

Answer 1

To find the coordinates of point \( P \), the intersection of the diagonals \( CE \) and \( DH \) in parallelogram \( CDEH \), we can use the midpoint formula. The diagonals of a parallelogram bisect each other, so we can find the midpoints of both diagonals.

First, we need to find the midpoints of diagonals \( CE \) and \( DH \).

### Midpoint of diagonal \( CE \):
The coordinates of points \( C \) and \( E \) are:
- \( C(-5, 5) \)
- \( E(-1, -1) \)

The formula for the midpoint \( M \) of a segment with endpoints \( (x_1, y_1) \) and \( (x_2, y_2) \) is:
\[
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]

Applying this to \( C \) and \( E \):
\[
M_{CE} = \left( \frac{-5 + (-1)}{2}, \frac{5 + (-1)}{2} \right) = \left( \frac{-6}{2}, \frac{4}{2} \right) = (-3, 2)
\]

### Midpoint of diagonal \( DH \):
The coordinates of points \( D \) and \( H \) are:
- \( D(2, 5) \)
- \( H(-8, -1) \)

Applying the midpoint formula again:
\[
M_{DH} = \left( \frac{2 + (-8)}{2}, \frac{5 + (-1)}{2} \right) = \left( \frac{-6}{2}, \frac{4}{2} \right) = (-3, 2)
\]

### Conclusion:
The coordinates of point \( P \), the intersection of the diagonals \( CE \) and \( DH \), are:
\[
P = (-3, 2)
\]

Thus, the coordinates of \( P \) are \((-3, 2)\).