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:
[tex]Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)[/tex]
In parallelogram GHJK ,
Midpoint of diagonal GJ = Midpoint of diagonal HK
[tex]\left(\dfrac{0+5}{2},\dfrac{8+2}{2}\right)=\left(\dfrac{a+1}{2},\dfrac{b+2}{2}\right)[/tex]
[tex]\left(\dfrac{5}{2},\dfrac{10}{2}\right)=\left(\dfrac{a+1}{2},\dfrac{b+2}{2}\right)[/tex]
On comparing both sides, we get
[tex]\dfrac{5}{2}=\dfrac{a+1}{2}[/tex]
[tex]5=a+1[/tex]
[tex]5-1=a[/tex]
[tex]4=a[/tex]
And,
[tex]\dfrac{10}{2}=\dfrac{b+2}{2}[/tex]
[tex]10=b+2[/tex]
[tex]10-2=b[/tex]
[tex]8=b[/tex]
Therefore, the coordinates of the vertex H are (4,8). Hence, option B is correct.
