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

The coordinates are 3,7 :)

Try thinking about partitioning a line segment

Answer 2

The coordinates of point B are (3 , 7)

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=(x_(1)m_(2)+x_(2)m_(1))/(m_(1)+m_(2))` and

`y=(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=((-5)(1)+x_(2)(3))/(3+1)`

∴
`1=(-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=((3)(1)+y_(2)(3))/(3+1)`

∴
`6=(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)