Question

Let AB be the directed line segment beginning at point A(2 , 3) and ending at point B(10 , 18). Find the point P on the line segment that partitions the line segment into the segments AP and PB at a ratio of 1:3.

Answer 1

Point P, which divides the directed line segment AB into segments AP and PB at a ratio of 1:3, has coordinates (4, 6.75).

Step-by-step explanation:

We need to find point P such that it divides the line segment AB into the ratio 1:3. The coordinates for points A and B are A(2, 3) and B(10, 18) respectively. According to the section formula, the coordinates of point P (x, y) that divides AB in the ratio 1:3 can be determined as follows:

x = (m*x2 + n*x1) / (m + n)

y = (m*y2 + n*y1) / (m + n)

where m:n is the ratio, x1, y1 are the coordinates of point A, and x2, y2 are the coordinates of point B.

By substituting the values of m, n, A, and B we get:

x = (1*10 + 3*2) / (1 + 3) = (10 + 6) / 4 = 16 / 4 = 4

y = (1*18 + 3*3) / (1 + 3) = (18 + 9) / 4 = 27 / 4 = 6.75

Therefore, the coordinates of point P are (4, 6.75).