Question

line segment AB has endpoints A (7.5, 4.2) and B (2.3 ,5.4). Find the coordinates of the point that divides the line segment directed from A to B in the ratio of 1:3.

Answer 1

(6.2, 4.5)

Explanation:

This can be solved using section formula, shown below:

`x=(mx_2+nx_1)/(m+n)`

and

`y=(my_2+ny_1)/(m+n)`

Where m and n are the ratio segmentation. Hence,

m = 1

n = 3

The points of x_1, x_2, y_1, and y_2 are given point respectively.

A(7.5, 4.2)

B(2.3, 5.4)

Thus, we have:

`x=(mx_2+nx_1)/(m+n)\\x=((1)(2.3)+(3)(7.5))/(1+3)\\x=6.2`

and

`y=(my_2+ny_1)/(m+n)\\y=((1)(5.4)+(3)(4.2))/(1+3)\\y=4.5`

The coordinates are (6.2, 4.5)