Question

Find the coordinates of the intersection of the diagonals of parallelogram HJKL with the given vertices: H(-1, 4), J(3, 3), K(3, -2), L(-1, -1). (Drawing a picture helps!)
thank you!

Answer 1

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:

$\sf \overline{HJ} \parallel \overline{LK}\:\: \textsf{ and }\:\: \overline{LK} \parallel \overline{HL}$

Therefore, the diagonals of the parallelogram are:

$\sf \overline{LJ} \:\: \textsf{ and }\:\:\overline{HK}$

To find the coordinates of the intersection of the diagonals, either:

1. draw a diagram (see attached) and determine the point of intersection of the diagonals from the diagram, or
2. 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

$\textsf{Midpoint}=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)\quad \textsf{where}\:(x_1,y_1)\:\textsf{and}\:(x_2,y_2)\:\textsf{are the endpoints}}\right)$

To find the midpoint of diagonal LJ, define the endpoints:

• $(x_1,y_1)=L=(-1, -1)$
• $(x_2,y_2)=J=(3,3)$

Substitute the defined endpoints into the formula and solve:

$\begin{aligned} \implies \textsf{Midpoint of LJ} & =\left(\dfrac{3-1}{2},\dfrac{3-1}{2}\right)\\ & =\left(\dfrac{2}{2},\dfrac{2}{2}\right)\\ & =\left(1,1\right) \end{aligned}$

Therefore, the coordinates off the intersection of the diagonals of parallelogram HJKL are (1, 1).

Learn more about midpoints here:

brainly.com/question/27962681

Answer 2

Check the order

• HJKL

Means H,J and K,L are adjacent coordinates

Hence HK and JL are diagonals

We know diagonals of a parallelogram bisect each other so midpoint of any diagonal would be the intersection point

Midpoint of HK

• (x1+x2/2,y1+y2/2)
• (-1+3/2,4-2/2)
• (2/2,2/2)
• (1,1)