Question

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

Answer 1

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

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=(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))`

- 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=((-6)(3)+(10)(1))/(1+3)=(-18+10)/(4)=(-8)/(4)=-2`

∵
`y=((-3)(3)+(9)(1))/(1+3)=(-9+9)/(4)=(0)/(4)=0`

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