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

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)

Answer 2

Santiago was incorrect, as the point
`G` is located at
`(-(1)/(2), (1)/(2))`

Step-by-step explanation

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

If point
`G` lies
`(1)/(2)` of along the way
`\overline{HI}`, that means
`G` should be the midpoint of line
`\overline{HI}`.

Mid-point formula is:
`((x_(1)+x_(2))/(2),(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......

`((6+(-7))/(2),(7+(-6))/(2))\\ \\ =(-(1)/(2), (1)/(2))`

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

So, Santiago was incorrect, as the point
`G` is located at
`(-(1)/(2), (1)/(2))`