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

Answer:

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

Step-by-step 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 $x=\frac{x_{1}m_{2}+x_{2}m_{1}}{m_{1}+m_{2}}$ and

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

* 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

∴ $x=\frac{(6)(1)+(3)(2)}{2+1}=\frac{6+6}{3}=\frac{12}{3}=4$

∴ $y=\frac{(3)(1)+(9)(2)}{2+1}=\frac{3+18}{3}=\frac{21}{3}=7$

∵ 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)