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

Answer:

$G = (2,-1)$

$H = (9,1)$

Step-by-step 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:

$(3,3) = \frac{1}{2}(4 + x,7+y)$

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:

$(3,3) = \frac{1}{2}(-3 + x,5+y)$

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:

$H = (9,1)$