Integral of an exponential divided by a root function

[chaoseverlasting]

Homework Statement

Prove that the diagonals of a parallelogram bisect each other.

Homework Equations

I chose one vertex as the origin, one as a and one as b. The final vertex was a+b.

The Attempt at a Solution

The diagonals were $$\vec{r_1}=\vec{a}+\vec{b}$$ and $$\vec{r_2}=\vec{b}-\vec{a}$$. Where do I go from here? Can I assume that they go through the center of the parallelogram or do I have to prove that too?

 

[EnumaElish]

What is the definition of a vertex?

 

[chaoseverlasting]

Err... a point where two vectors intersect?

 

[HallsofIvy]

Your vectors "begin" at one vertex, right? What vector, starting at that vertex, has its "end" at the midpoint of $\vec{a}+ \vec{b}$? $\vec{b}-\vec{a}$?
(Note that, since $\vec{b}-\vec{a}$ "starts" at $\vec{a}$ instead of the origin, the midpoint of $\vec{b}-\vec{a}$ is at $\vec{a}$ plus half of $\vec{b}-\vec{a}$.)