Given:
A point divides a directed line segment from (-6, -3) to (5,8) into a ratio of 6 to 5.
To find:
The coordinates of that point.
Solution:
Section formula: If point divides a line segment in m:n, then the coordinates of that point are
[tex]Point=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)[/tex]
A point divides a directed line segment from (-6, -3) to (5,8) into a ratio of 6 to 5. Using section formula, we get
[tex]Point=\left(\dfrac{6(5)+5(-6)}{6+5},\dfrac{6(8)+5(-3)}{6+5}\right)[/tex]
[tex]Point=\left(\dfrac{30-30}{11},\dfrac{48-15}{11}\right)[/tex]
[tex]Point=\left(\dfrac{0}{11},\dfrac{33}{11}\right)[/tex]
[tex]Point=\left(0,3\right)[/tex]
Therefore, the coordinates of the required point are (0,3).