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
`(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
`((m_1x_2+m_2x_1)/(m_1+m_2) , (m_1y_2+m_2y_1)/(m_1+m_2) )`

Coordinates G =
`(((1 * -7)+(1 * 6))/(2) , ((1 * -6)+(1 * 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.