Question 1189872
the midpoint from point A to point B would be found by the formula:
midpoint = ((x1 + x2)/2, (y1 + y2)/2)


(x1,y1) = (-3,2)
(x2,y2) = (2,6)


midpoint is equal to ((-3 + 2)/2, (2 + 6)/2) which is equal to (-1/2,4).
this can also be shown as (-.5,4).


you will be camping at the point (-1/2, 4).
we'll call that point C.
point C is the midpoint between point A and point B.


on the first day, you will have hiked from the lodge to point A and then to point C.


the distance between the lodge and point A is equal to sqrt((-3)^2 + 2^2) = sqrt(9 + 4) = sqrt(13).


point A is at (-3,2).
point C is at (-.5,4).
-.5 - (-3) is equal to 2.5
4 - 2 is equal to 2
the distance between point A and point C is equal to sqrt(2.5^2 + 2^2) which is equal to sqrt(6.25 + 4) which is equal to sqrt(10.25).


the distance traveled from the lodge to point A and then to point C is therefore equal to sqrt13) + sqrt(10.25) = 6.807113394 kilometers.


if you continue in the same direction you were traveling to complete the loop from the lodge to point A to point B to the lodge, then you will be traveling from point C to point B to the lodge on the second day.


the distance from point C to point B is the same as the distance from point A to point C, which is equal to sqrt(10.25).


the distance between point B and the lodge is equal to sqrt(2^2 + 6^2) = sqrt(4 + 36) = sqrt(40).


the total distance you travel on the second day must be sqrt(10.25) + sqrt(40) = 9.526117439 kilometers.


your solution is that you stopped at the point (-.5,4) at the end of the first day and that you traveled 6.807113394 kilometers on the first day and 9.526117439 kilometers on the second day.


let me know if you have any questions.


theo