lucasturbo100
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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!

Sagot :

semsee45

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:

  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

[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

View image semsee45

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)
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