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

Answer:

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

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 the ratio $m_{1}:m_{2}$ from point

 $(x_{1},y_{1})$, 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 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 $m_{2}=3$

∴ $x=\frac{(-4)(3)+(8)(2)}{2+3}=\frac{-12+16}{5}=\frac{4}{5}$

∴ $y=\frac{(3)(3)+(-1)(2)}{2+3}=\frac{9+-2}{5}=\frac{7}{5}$

∵ 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)