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} ((x_2+x_1)/(2)),((y_2+y_1)/(2)) \\ BD=(-(1)/(2),(9)/(2)) \\ AC=(-(1)/(2),(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.