Hi I have a midterm this Friday, and our prof gave us this practice midterm, I got $6$ of the $10$ questions but couldn't do the last $4$, could you please help me out in this question, I have no idea how to approach it. Thank you.
a) Suppose a quadrilateral $ABCD$ in $\mathbb{R^2}$ is not a parallelogram. Use vectors to show that the segments connecting the midpoints of opposite sides and the line connecting the midpoints of the diagonals are concurrent.
b) What is the name of this point where the three segments meet?
