Question

- Segment CD has endpoints (-4, 3) and (8,-1). Find the coordinates of the point that divides the line segment

directed from C to D in the ratio of 2:3.
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Answer 1

The coordinates of the division point are (0.8 , 1.4)

Explanation:

* Lets explain how to find the point of division

- If point (x , y) divide the line whose endpoints are
`(x_(1),y_(1))`

and
`(x_(2),y_(2))` at the ratio
`m_(1):m_(2)` from 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))`

* Lets solve the problem

∵ The endpoint of CD are (-4 , 3) and (8 , -1)

∵ Point (x , y) divides CD directed from C to D at ratio 2 : 3

- By using the rule above

∵ Point (-4 , 3) is
`(x_(1),y_(1))`

∵ Point (8 , -1) is
`(x_(2),y_(2))`

∵
`m_(1)=2` and
`m_(2)=3`

∴
`x=((-4)(3)+(8)(2))/(2+3)=(-12+16)/(5)=(4)/(5)`

∴
`y=((3)(3)+(-1)(2))/(2+3)=(9+-2)/(5)=(7)/(5)`

∵ The x-coordinate of the point is 4/5 = 0.8

∵ The y-coordinate of the point is 7/5 = 1.4

∴ The coordinates of the division point are (0.8 , 1.4)