Question

Given H (6,7) and I (-7,6), if point G lies 1/2 of along the way HI, Santiago Argues That Point G Is Located At The Origin. Is Santiago Correct? Justify Your Answer.

Answer 1

Santiago was incorrect, as the point $G$ is located at $(-\frac{1}{2}, \frac{1}{2})$

Explanation

The co ordinates of the given points are:   $H(6,7)$ and $I(-7,-6)$

If point $G$ lies $\frac{1}{2}$ of along the way $\overline{HI}$, that means $G$ should be the midpoint of line $\overline{HI}$.

Mid-point formula is:  $(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$ , where $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ are two endpoints.

So, the co ordinate of the midpoint of $H$ and $I$ will be......

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

Co ordinate of the origin is always $(0,0)$

So, Santiago was incorrect, as the point $G$ is located at $(-\frac{1}{2}, \frac{1}{2})$

Answer 2

If G is halfway, then it is the midpoint..
midpoint formula : (x1 + x2)/2 , (y1 + y2)/2
(6,7)....x1 = 6 and y1 = 7
(-7,-6)....x2 = -7 and y2 = -6
now we sub
m = (6 - 7) / 2 , (7 - 6)/2
m = (-1/2 , 1/2)

Santiago is wrong. Point G lies at (-1/2,1/2)