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 \((-3, 2)\).
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