Question

What is the point of intersection of the diagonals of the parallelogram `MOPS` with vertices `M (-8,3), O(2,3), P (4,-5),` and `S (-6,-5)`?

Answer 1

Point of intersection of diagonals of parallelogram `MOPS` is `(-2,4)`

Explanation:

As the ordinates of point `M` and `O` are same, `MO` is parallel to `x`-axis and has length of `2-(-8)=10`.

Also as ordinates of point `P` and `S` are same, `PS` is parallel to `x`-axis and has length of `4-(-6)=10`.

As such, as `MO||PS` and `MO=PS` and `MOPS` is a parallelogram.

and point of intersection of diagonals will be mid point of

either midpoint of `MP`, which is `((-8+4)/2,(3-(-5))/2)` or `(-2,4)`

or midpoint of `OS`, which is `((2-6)/2,(3-(-5))/2)` or `(-2,4)`.