Question

Given points A(-8, -10) and B(2, 10), find the point that divides the line segment AB four-fifths of the way from A to B.

A) (-2, 2)
B) (-4, 4)
C) (0, 0)

Answer 1

The point that divides the line segment AB four-fifths of the way from A to B is calculated using the section formula, resulting in the point (-1.6, 6), which does not match any of the given options.

Step-by-step explanation:

The student has asked for the point that divides the line segment AB four-fifths of the way from A to B. This involves finding a point on the segment that is in a 4:1 ratio, with the larger portion being closest to point A. To solve this problem, we can apply the section formula which is an application of the weighted average:

• Let A be (-8, -10) and B be (2, 10).
• The formula to find point P that divides AB in the ratio m:n is P(x,y) = ((mx2 + nx1)/(m + n), (my2 + ny1)/(m + n)).
• The ratio, in this case, is 4:1 where P is the point we are seeking.
• Thus, P(x,y) = ((4*2 + 1*(-8))/(4 + 1), (4*10 + 1*(-10))/(4 + 1)).
• After calculation, P(x,y) = (-8/5, 30/5) = (-1.6, 6).

However, the given options to choose from are A) (-2, 2), B) (-4, 4), and C) (0, 0).