Becky is writing a coordinate proof to show that the diagonals of a parallelogram bisect each other. she starts by assigning coordinates as given .

Proved.

Step-by-step explanation:

Given that coordinates of A, B and D are (0,0) (a,0) and (b,c) respectively

C is having y coordinate same as D but x coordinate will be a+b

(a+b,c) is C

Now the mid point of AC is using mid point formula

to prove that the diagonals bisect each other it is sufficient to show that

The coordinates of the midpoint of diagonal BD=

Since we have B = (1,0) and D = (b,c)

using mid point formula we get mid point of BD

=

Comparing these two we find the mid point is the same for both the diagonals.

In other words, in a parallelogram diagonals bisect each other,