Question

Given H(6,7) and I(-7,-6), if point G lies 1/2 of the way along line segment HI, Santiago argues that point G is located at the origin. Is Santiago correct? Justify your answer.

Answer 1

Given the points H(6,7) and I(-7,-6).

If point G lies $\frac{1}{2}$ 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 $(x_1, y_1)$ and $(x_2, y_2)$ divided is in the ratio $m_1 : m_2$, the coordinates are $(\frac{m_1x_2+m_2x_1}{m_1+m_2} , \frac{m_1y_2+m_2y_1}{m_1+m_2} )$

Coordinates G = $(\frac{(1 \times -7)+(1 \times 6)}{2} , \frac{(1 \times -6)+(1 \times 7)}{2})$

= (-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.