Answer:
The coordinates of point B are (3 , 7)
Step-by-step explanation:
* Lets explain how to solve the problem
- If point (x , y) divides a line segments whose endpoints are [tex](x_{1},y_{1})[/tex]
and [tex](x_{2},y_{2})[/tex] at ratio [tex](m_{1}:m_{2})[/tex] from the first point [tex](x_{1},y_{1})[/tex], 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]
∵ Point A = (-5 , 3)
∵ The point of dinision (x , y) = (1 , 6)
∵ Point B = [tex](x_{2},y_{2})[/tex]
- Point (1, 6) is 3/4 of the way from A to B, that means the distances
from A to (1 , 6) is 3 parts and from (1 , 6) to B is (4 - 3) = 1 part
∴ [tex](m_{1}:m_{2})[/tex] = 3 : 1
∵ [tex]1=\frac{(-5)(1)+x_{2}(3)}{3+1}[/tex]
∴ [tex]1=\frac{-5+3x_{2}}{4}[/tex]
- Multiply each side by 4
∴ [tex]4=-5+3x_{2}[/tex]
- Add 5 to both sides
∴ [tex]9=3x_{2}[/tex]
- Divide both sides by 3
∴ [tex]x_{2}=3[/tex]
∴ The x-coordinate ob point B is 3
∵ [tex]6=\frac{(3)(1)+y_{2}(3)}{3+1}[/tex]
∴ [tex]6=\frac{3+3y_{2}}{4}[/tex]
- Multiply each side by 4
∴ [tex]24=3+3y_{2}[/tex]
- Subtract 3 to both sides
∴ [tex]21=3y_{2}[/tex]
- Divide both sides by 3
∴ [tex]y_{2}=7[/tex]
∴ The y-coordinate ob point B is 7
* The coordinates of point B are (3 , 7)
