Answer:
The coordinates of point E are (3,-2)
Step-by-step explanation:
we know that
The diagonals of a parallelogram bisect each other
That means ----> The coordinates of point E is the midpoint diagonal AC or the midpoint diagonal BD
The formula to calculate the midpoint between two points is equal to
[tex]M=(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]
Verify both cases
Find the midpoint AC
we have the points
A(1,1) and C(5,-5)
substitute in the formula
[tex]E=(\frac{1+5}{2},\frac{1-5}{2})[/tex]
[tex]E=(3,-2)[/tex]
Find the midpoint BD
we have the points
B(8,5) and D (-2,-9)
substitute in the formula
[tex]E=(\frac{8-2}{2},\frac{5-9}{2})[/tex]
[tex]E=(3,-2)[/tex]
therefore
The coordinates of point E are (3,-2)
