Question

On parallelogram ABCD below, if A(1,1) B(8,5) C(5,-5) and D (-2,-9), what are the coordinates of point E?

Answer 1

The coordinates of point E are (3,-2)

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

`M=((x1+x2)/(2),(y1+y2)/(2))`

Verify both cases

Find the midpoint AC

we have the points

A(1,1) and C(5,-5)

substitute in the formula

`E=((1+5)/(2),(1-5)/(2))`

`E=(3,-2)`

Find the midpoint BD

we have the points

B(8,5) and D (-2,-9)

substitute in the formula

`E=((8-2)/(2),(5-9)/(2))`

`E=(3,-2)`

therefore

The coordinates of point E are (3,-2)