Question

point A has coordinates (-5, 3). If point (1, 6) is 3/4 of the way from A to B, what are the coordinates of point B​

Answer 1

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 $(x_{1},y_{1})$

  and $(x_{2},y_{2})$ at ratio $(m_{1}:m_{2})$ from the first point $(x_{1},y_{1})$, then

  $x=\frac{x_{1}m_{2}+x_{2}m_{1}}{m_{1}+m_{2}}$ and

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

∵ Point A = (-5 , 3)

∵ The point of dinision (x , y) = (1 , 6)

∵ Point B =  $(x_{2},y_{2})$

- 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

∴ $(m_{1}:m_{2})$ = 3 : 1

∵ $1=\frac{(-5)(1)+x_{2}(3)}{3+1}$

∴ $1=\frac{-5+3x_{2}}{4}$

- Multiply each side by 4

∴ $4=-5+3x_{2}$

- Add 5 to both sides

∴ $9=3x_{2}$

- Divide both sides by 3

∴ $x_{2}=3$

∴ The x-coordinate ob point B is 3

∵ $6=\frac{(3)(1)+y_{2}(3)}{3+1}$

∴ $6=\frac{3+3y_{2}}{4}$

- Multiply each side by 4

∴ $24=3+3y_{2}$

- Subtract 3 to both sides

∴ $21=3y_{2}$

- Divide both sides by 3

∴ $y_{2}=7$

∴ The y-coordinate ob point B is 7

* The coordinates of point B are (3 , 7)

Answer 2

Answer:

The coordinates are 3,7 :)

Try thinking about partitioning a line segment