Final answer:
The point that divides the line segment AB in the ratio 2:6, with A(-6,9) and B(6,-7), is found using the section formula and has coordinates (-3,5), which is not listed in the given options.
Step-by-step explanation:
To find the coordinates of a point that divides a line segment AB in the ratio 2:6, we use the section formula. The coordinates of points A and B are given as A(-6,9) and B(6,-7). The section formula for a point (x, y) that divides a line segment AB in the ratio m:n is given by:
x = (mx2 + nx1) / (m + n)
y = (my2 + ny1) / (m + n)
Substituting the values, we get:
x = (2*6 + 6*(-6)) / (2 + 6) = (12 - 36) / 8 = -24 / 8 = -3
y = (2*(-7) + 6*9) / (2 + 6) = (-14 + 54) / 8 = 40 / 8 = 5
The coordinates of the point that divides the line segment AB in the ratio 2:6 is (-3,5), which is not one of the options provided. Therefore, there may be an error in the question or the provided options.