To find the point that is exactly halfway in-between Kylie and Reuben along the slope of the mountain, we need to determine the midpoint of the line segment connecting them.
Let's assume that Kylie is located at point A and Reuben is located at point B. Then, the midpoint M of the line segment AB can be found by using the midpoint formula:
M = ((x1 + x2)/2, (y1 + y2)/2)
where (x1, y1) and (x2, y2) are the coordinates of points A and B, respectively.
Since the mountain slope is uniform, we can assume that the line connecting Kylie and Reuben is a straight line. Therefore, we can use the coordinates of the two points to find the equation of the line in slope-intercept form:
y = mx + b
where m is the slope of the line and b is the y-intercept.
To find the slope of the line, we can use the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are the coordinates of points A and B, respectively.
Let's assume that Kylie is located at point (x1, y1) = (a, b) and Reuben is located at point (x2, y2) = (c, d). Then, the slope of the line can be calculated as:
m = (d - b) / (c - a)
Once we have the slope of the line, we can find the y-intercept b by substituting the coordinates of one of the points (e.g., point A) and the slope into the slope-intercept equation:
b = y1 - mx1
Now we have the equation of the line in slope-intercept form, so we can find the coordinates of the midpoint M by plugging in the x-coordinate of the midpoint and solving for the y-coordinate:
M = ((a + c)/2, (b + d)/2)
Therefore, the point that is exactly halfway in-between Kylie and Reuben along the slope of the mountain is M = ((a + c)/2, (b + d)/2).