Given the points H(6,7) and I(-7,-6).
If point G lies [tex]\frac{1}{2}[/tex] of the way along line segment HI.
Therefore, we can say that the point G divides the line segment HI in the ratio 1:1.
So, by using the cross section formula we can determine the coordinates of point G.
For the given points say [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] divided is in the ratio [tex]m_1 : m_2[/tex], the coordinates are [tex](\frac{m_1x_2+m_2x_1}{m_1+m_2} , \frac{m_1y_2+m_2y_1}{m_1+m_2} )[/tex]
Coordinates G = [tex](\frac{(1 \times -7)+(1 \times 6)}{2} , \frac{(1 \times -6)+(1 \times 7)}{2})[/tex]
= (-0.5 , 0.5)
Hence, the coordinates of G are (-0.5 , 0.5).
So, Santiago argues that point G is located at the origin. The point G is located at (-0.5, 0.5). Therefore, he is not correct.
