Answer:
The coordinates of the point are (-2 , 0)
Step-by-step explanation:
* Lets explain how to solve the problem
- If point (x , y) divides a line segment whose end points are
[tex](x_{1},y_{1})[/tex] and [tex](x_{1},y_{1})[/tex] at ratio [tex]m_{1}:m_{2}[/tex]
from the first point, then [tex]x=\frac{x_{1}m_{2}+x_{2}m_{1}}{m_{1}+m_{2}}[/tex]
and [tex]y=\frac{y_{1}m_{2}+y_{2}m_{1}}{m_{1}+m_{2}}[/tex]
- Let point A (-6 , -3) is point [tex](x_{1},y_{1})[/tex]
- Let point B (10 , 9) is point [tex](x_{2},y_{2})[/tex]
- Let The point of division is (x , y)
∵ The point of division is located at 1/4 from A to B
∴ From A to (x , y) is 1 part and from (x , y) to B is (4 - 1) = 3 parts
∴ [tex]m_{1}:m_{2}=1:3[/tex]
∵ [tex]x=\frac{(-6)(3)+(10)(1)}{1+3}=\frac{-18+10}{4}=\frac{-8}{4}=-2[/tex]
∵ [tex]y=\frac{(-3)(3)+(9)(1)}{1+3}=\frac{-9+9}{4}=\frac{0}{4}=0[/tex]
∴ The coordinates of the point are (-2 , 0)
