Answer:
(1, 1)
Step-by-step explanation:
Given vertices of the parallelogram:
- H = (-1, 4)
- J = (3, 3)
- K = (3, -2)
- L = (-1, -1)
Therefore the parallel sides are:
[tex]\sf \overline{HJ} \parallel \overline{LK}\:\: \textsf{ and }\:\: \overline{LK} \parallel \overline{HL}[/tex]
Therefore, the diagonals of the parallelogram are:
[tex]\sf \overline{LJ} \:\: \textsf{ and }\:\:\overline{HK}[/tex]
To find the coordinates of the intersection of the diagonals, either:
- draw a diagram (see attached) and determine the point of intersection of the diagonals from the diagram, or
- determine the midpoint of either diagonal (as the diagonals of a parallelogram bisect each other, i.e. divide into 2 equal parts).
Midpoint between two points
[tex]\textsf{Midpoint}=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)\quad \textsf{where}\:(x_1,y_1)\:\textsf{and}\:(x_2,y_2)\:\textsf{are the endpoints}}\right)[/tex]
To find the midpoint of diagonal LJ, define the endpoints:
- [tex](x_1,y_1)=L=(-1, -1)[/tex]
- [tex](x_2,y_2)=J=(3,3)[/tex]
Substitute the defined endpoints into the formula and solve:
[tex]\begin{aligned} \implies \textsf{Midpoint of LJ} & =\left(\dfrac{3-1}{2},\dfrac{3-1}{2}\right)\\ & =\left(\dfrac{2}{2},\dfrac{2}{2}\right)\\ & =\left(1,1\right) \end{aligned}[/tex]
Therefore, the coordinates off the intersection of the diagonals of parallelogram HJKL are (1, 1).
Learn more about midpoints here:
https://brainly.com/question/27962681
