Final answer:
The point (-1, 6) does not divide the line segment joining the points (-3, 10) and (6, -8) in a 2:1 inverse ratio; the calculated point using the section formula is (0, 4), which does not match (-1, 6). Therefore, the answer is false.
Step-by-step explanation:
The student's question concerns whether the point (-1, 6) divides the line segment joining the points (-3, 10) and (6, -8) in a 2:1 ratio inversely. To determine if this is true, we can use the formula for internal division of a point in a given ratio on a line segment. According to the section formula, if a point P(x, y) divides the line segment joining A(x1, y1) and B(x2, y2) in the ratio m:n, then P's coordinates are given by:
((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n)).
For an inverse ratio 2:1, we consider the ratio as 1:2. Using the coordinates A(-3, 10) and B(6, -8), and applying the section formula for P(-1, 6), we have:
x-coordinate: ((1×6 + 2×(-3))/(1+2) = (6 - 6)/3 = 0/-1)
y-coordinate: ((1×(-8) + 2×10)/(1+2) = (-8 + 20)/3 = 12/3 = 4)
The computed coordinates (0, 4) do not match the given point (-1, 6); therefore, the point (-1, 6) does not divide the line segment in a 2:1 inverse ratio. Hence, the correct answer is false.