Question

Line segment AB has endpoints A(6, 1) and B(3, 8). Find the coordinates of the point that divides the line segment directed from A to B in the ratio of 2:3.

Answer 1

Answer:

(4.8,3.8)

Step-by-step explanation:

We want to find the coordinates of the point that divides A(6, 1) and B(3, 8) in the ratio m:n=2:3

We use the section formula:

$(\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n})$

Let us substitute the points and the ratio to get:

$(\frac{2 \times 3+3 \times 6}{2 + 3},\frac{2 \times 8+3 \times 1}{2+3})$

This simplifies to:

$(\frac{6+18}{5},\frac{16+3}{5})$

$(\frac{24}{5},\frac{19}{5})$

The coordinates are (4.8,3.8)