Hi!
I would approach this question by first looking at where the parallelogram is located, by graphing the image. I did so and drew a rough image on Paint (See attached image)
To get the part where the diagonals intersect, I would find the midpoint of the line between points (1, 3) and (5,-9) (or the other pair). The reason is a parallelogram's diagonals always bisect each other, meaning the point they intersect is always the middle of the two diagonals.
Therefore, you can find the midpoint of a diagonal, between (1, 3) and (5, -9). The midpoint theorem is ([tex] \frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2} [/tex].
Take the points (1, 3) and (5, -9), and fill them in.
[tex] (\frac{1 + 5}{2} , \frac{3 - 9}{2}) [/tex]
Then solve.
[tex] (\frac{6}{2}, \frac{-6}{2}) [/tex]
(3, -3)
If you'd like to check the other midpoint:
Take the points, (8, 3) and (-2, -9)
[tex] (\frac{8 - 2}{2}, \frac{3 - 9}{2}) [/tex]
Then solve.
[tex] (\frac{6}{2} , \frac{-6}{2}) [/tex]
(3, -3)
They're the same, so that answer is correct.
Hope this helps!
