Please help ASAP!!! THANKS!

Question

asked Sep 13, 2022 197k views

1 Answer

Akrion · Answer 1 · 2022-09-20T08:51:34+0000

Given:

The vertices of a parallelogram GHJK are K(1,2), J(5,2), G(0,8).

To find:

The coordinate of the vertex H.

Solution:

We know that the diagonals of a parallelogram bisects each other. It means the midpoint of the diagonals are same.

Let the coordinate of the vertex H are (a,b).

Midpoint formula:

$Midpoint=\left((x_1+x_2)/(2),(y_1+y_2)/(2)\right)$

In parallelogram GHJK ,

Midpoint of diagonal GJ = Midpoint of diagonal HK

$\left((0+5)/(2),(8+2)/(2)\right)=\left((a+1)/(2),(b+2)/(2)\right)$

$\left((5)/(2),(10)/(2)\right)=\left((a+1)/(2),(b+2)/(2)\right)$

On comparing both sides, we get

(5)/(2)=(a+1)/(2)

5=a+1

5-1=a

4=a

And,

(10)/(2)=(b+2)/(2)

10=b+2

10-2=b

8=b

Therefore, the coordinates of the vertex H are (4,8). Hence, option B is correct.