Question

What are the coordinates 1/4 of the way from A(-6,-3) to B(10,9)?

Answer 1

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

 $(x_{1},y_{1})$ and $(x_{1},y_{1})$ at ratio $m_{1}:m_{2}$

 from the first point, then $x=\frac{x_{1}m_{2}+x_{2}m_{1}}{m_{1}+m_{2}}$

 and $y=\frac{y_{1}m_{2}+y_{2}m_{1}}{m_{1}+m_{2}}$

- Let point A (-6 , -3) is point $(x_{1},y_{1})$

- Let point B (10 , 9) is point $(x_{2},y_{2})$

- 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

∴ $m_{1}:m_{2}=1:3$

∵ $x=\frac{(-6)(3)+(10)(1)}{1+3}=\frac{-18+10}{4}=\frac{-8}{4}=-2$

∵ $y=\frac{(-3)(3)+(9)(1)}{1+3}=\frac{-9+9}{4}=\frac{0}{4}=0$

∴ The coordinates of the point are (-2 , 0)