Question

Please help ASAP!!! THANKS!

Answer 1

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:

$Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)$

In parallelogram GHJK ,

Midpoint of diagonal GJ = Midpoint of diagonal HK

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

$\left(\dfrac{5}{2},\dfrac{10}{2}\right)=\left(\dfrac{a+1}{2},\dfrac{b+2}{2}\right)$

On comparing both sides, we get

$\dfrac{5}{2}=\dfrac{a+1}{2}$

$5=a+1$

$5-1=a$

$4=a$

And,

$\dfrac{10}{2}=\dfrac{b+2}{2}$

$10=b+2$

$10-2=b$

$8=b$

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