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

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

$M=(\frac{x1+x2}{2},\frac{y1+y2}{2})$

Verify both cases

Find the midpoint AC

we have the points

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

substitute in the formula

$E=(\frac{1+5}{2},\frac{1-5}{2})$

$E=(3,-2)$

Find the midpoint BD

we have the points

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

substitute in the formula

$E=(\frac{8-2}{2},\frac{5-9}{2})$

$E=(3,-2)$

therefore

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