Given:
A segments is from (−6,−1) to (6, -9).
A point divides the line segment into a ratio of 3 to 1.
To find:
The coordinates of the points.
Solution:
Section formula: If a point divides a line segment in m:n, then
[tex]Point=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)[/tex]
The point divides the line segment in 3:1, so by using section formula, we get
[tex]Point=\left(\dfrac{3(6)+1(-6)}{3+1},\dfrac{3(-9)+1(-1)}{3+1}\right)[/tex]
[tex]Point=\left(\dfrac{18-6}{4},\dfrac{-27-1}{4}\right)[/tex]
[tex]Point=\left(\dfrac{12}{4},\dfrac{-28}{4}\right)[/tex]
[tex]Point=\left(3,-7\right)[/tex]
Therefore, the coordinates of the required point are (3,-7).
