Question

Segment YZ has endpoints (6,3) and (3,9). Find the coordinates of the point that divides the line segment directed

from Y to Z in the ratio of 2:1.
A)
. (4,6)
June
C)
(5, 4)
11:38 AM
8/28/20193
to search

Answer 1

The coordinates of the division point are (4 , 7)

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 ratio
`m_(1):m_(2)` from Y to Z

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 YZ are (6 , 3) and (3 , 9)

∵ Point (x , y) divides YZ directed from Y to Z at ratio 2 : 1

- By using the rule above

∵ Point (6 , 3) is
`(x_(1),y_(1))`

∵ Point (3 , 9) is
`(x_(2),y_(2))`

∵
`m_(1):m_(2)` = 2 : 1

∴
`x=((6)(1)+(3)(2))/(2+1)=(6+6)/(3)=(12)/(3)=4`

∴
`y=((3)(1)+(9)(2))/(2+1)=(3+18)/(3)=(21)/(3)=7`

∵ The x-coordinate of the point is 4

∵ The y-coordinate of the point is 7

∴ The coordinates of the division point are (4 , 7)