Answer:
Point of intersection is (-2, -1).
Step-by-step explanation:
The diagonals bisect each other so we only need to find the midpoint of one of the diagonals. We'll use the diagonal qs:-
Midpoint = (-8 + 4)/2, (1 + -3)/2
= (-2, -1)
Parallelograms have equal and parallel opposite sides.
The intersection of the diagonal is at (-2,-1).
The coordinates are given as:
[tex]\mathbf{q = (-8,1)}[/tex]
[tex]\mathbf{r = (2,1)}[/tex]
[tex]\mathbf{s = (4,-3)}[/tex]
[tex]\mathbf{t = (-6,-3)}[/tex]
The diagonals are: qs and rt.
Calculate the midpoint of qs, as follows:
[tex]\mathbf{qs = (\frac{-8 + 4}{2},\frac{1-3}{2})}[/tex]
[tex]\mathbf{qs = (\frac{-4}{2},\frac{-2}{2})}[/tex]
[tex]\mathbf{qs = (-2,-1)}[/tex]
Calculate the midpoint of rt, as follows:
[tex]\mathbf{rt = (\frac{2 - 6}{2},\frac{1-3}{2})}[/tex]
[tex]\mathbf{rt = (\frac{ - 4}{2},\frac{-2}{2})}[/tex]
[tex]\mathbf{rt = (-2,-1)}[/tex]
Hence, the intersection of the diagonal is at (-2,-1).
Read more about diagonals of parallelogram at:
https://brainly.com/question/21993509
