Question

The diagonals of quadrilateral EFGH intersect at D(3,3). EFGCH has vertices at E(4,7) and F(-3,5). What must be the coordinates of G and H to ensure that EFGH is a parallelogram.

Answer 1

`G = (2,-1)`

`H = (9,1)`

Explanation:

Given

`E = (4,7)`

`F=(-3,5)`

`D =(3,3)` --- Diagonal

Required

Determine the coordinates of G and H

Since EFGH is a parallelogram, then:

D is the midpoint of EG and EF

For EG, we have:

`(3,3) = (1)/(2)(4 + x,7+y)`

Where x, y are the coordinates of G.

Multiply both sides by 2

`(6,6) = (4+x,7+y)`

By comparison:

`4 + x = 6` ==>
`x =2`

`7 + y= 6` ==>
`y = -1`

So:

`G = (2,-1)`

For FH, we have:

`(3,3) = (1)/(2)(-3 + x,5+y)`

Where x, y are the coordinates of H.

Multiply both sides by 2

`(6,6) = (-3 + x,5+y)`

By comparison:

`-3+x = 6` ==>
`x = 9`

`5 + y = 6` ==>
`y =1`

So:

`H = (9,1)`