Question

23. Find te point of intersection ofthe diagonals of the paralelogramMOPS with vertices M(-8,3), O(2,3),P(4,-5), and S(-6,-5).

Answer 1

Step-by-step explanation

As we already know that the ordinates of the points M and O are the same, MO is parallel to the x-axis and also PS.

The length of both segments (MO and PS is the same and equal to MO = 2 - (-8) = 10 and PS = 4 - (-6 ) = 10 )

Know, we know that MO and PS are parallel segments and with the same length, the point of intersection of the diagonals will be the midpoint MP and OS, and we can compute them as follows:

`midpoint_(MP)=((-8+4)/(2),(3-5)/(2))=(-2,-1)`
`midpoint_(OS)=((2-6)/(2),(3-5)/(2))=(-2,-1)`

In conclusion, the point of intersection is (-2,-1)

Now, we can represent the parallelogram on a graph as follows: