Given:
Two points are (6, 7) and I(-7,-6).
Point G lies [tex]\dfrac{1}{2}[/tex] of the way along Hl.
John says that point G is located at the origin.
To find:
Whether John is correct or not.
Solution:
Point G lies [tex]\dfrac{1}{2}[/tex] of the way along Hl. I means point G is the midpoint of HI.
[tex]Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)[/tex]
[tex]G=\left(\dfrac{6-7}{2},\dfrac{7-6}{2}\right)[/tex]
[tex]G=\left(\dfrac{-1}{2},\dfrac{1}{2}\right)[/tex]
The location of point G is at [tex]\left(\dfrac{-1}{2},\dfrac{1}{2}\right)[/tex], which is not equal to origin, i.e., (0,0).
Therefore, John is incorrect.
