Question

Explain how to use the midpoint formula to prove or disapprove that ABCD is a parallelogram

Answer 1

Step 1

The property of a parallelogram is that diagonals of a parallelogram bisect each other and hence have the same midpoint.

This means that the diagonals cut themselves into two equal halves.

Hence, they must have the same mid-points.

Therefore, if we prove that AC and BD have the same midpoint, then ABCD is a parallelogram.

Step 2

Find the midpoint of BD and AC

$\begin{gathered} (\frac{x_2+x_1}{2}),(\frac{y_2+y_1}{2}) \\ BD=(-\frac{1}{2},\frac{9}{2}) \\ AC=(-\frac{1}{2},\frac{9}{2}) \end{gathered}$

Since they have the same midpoint, the answer will be;

We Prove that AC and BD have the same midpoint which we have done. we know the diagonals of a parallelogram bisect each other; therefore, they have the same midpoint and ABCD is a parallelogram.