SOLUTION: Write a coordinate proof to show that the segments connecting the midpoints of any quadrilateral form a parallelogram. I think it is simpler to use vectors but not sure if I have t

Question 1206128: Write a coordinate proof to show that the segments connecting the midpoints of any quadrilateral form a parallelogram. I think it is simpler to use vectors but not sure if I have to use midpoint formulas. Thank you.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Let the coordinates of the vertices of the quadrilateral be

A(2a,2b)
B(2c,2d)
C(2e,2f)
D(2g,2h)

The midpoints are

AB: P(a+c,b+d)
BC: Q(c+e,d+f)
CD: R(e+g,f+h)
DA: S(g+a,h+b)

Opposite sides PQ and RS have the same slope:
PQ:
RS:

And opposite side QR and PS have the same slope:
QR:
PS:

Both pairs of opposite sides are parallel, making the quadrilateral a parallelogram.

RELATED QUESTIONS
Please help! Problem: "Prove that the figure formed by connecting the midpoints of the... (answered by venugopalramana)

write a corrdinate proof to show that the three segments joining the midpoints of the... (answered by richard1234)

Prove that the quadrilateral formed by connecting the midpoints of the sides of... (answered by ikleyn,Edwin McCravy)

How do you prove that the midpoints of quadrilateral will form a parallelogram using a... (answered by solver91311)

Write a coordinate proof for each statement. The three segments joining the midpoints of... (answered by Edwin McCravy)

the midpoint quadrilateral theorem: the quadrilateral formed bt joining the midpoints of... (answered by robertb)

Prove that midpoints of a quadrilateral form a... (answered by acalgebra)

Use the coordinate plane, the figure below, coordinate proof strategies, and the lengths... (answered by math1745)