The coordinates of the point that divides the line segment directed
from A to B in the ratio of 1 : 2 are ( [tex]6\frac{2}{3}[/tex] , 4)
Step-by-step explanation:
If point (x , y) divides a line segment whose endpoints are [tex](x_{1},y_{1})[/tex]
and [tex](x_{2},y_{2})[/tex] at ratio [tex]m_{1}:m_{2}[/tex] from [tex](x_{1},y_{1})[/tex] , then
- [tex]x=\frac{x_{1}m_{2}+x_{2}m_{1}}{m_{1}+m_{2}}[/tex]
- [tex]y=\frac{y_{1}m_{2}+y_{2}m_{1}}{m_{1}+m_{2}}[/tex]
∵ Line segment AB has endpoints A(9 , 3) and B(2 , 6)
∵ Point (x , y) divides the line segment from A to B in the ratio of 1 : 2
∴ [tex]x_{1}[/tex] = 9 and [tex]y_{1}[/tex] = 3
∴ [tex]x_{2}[/tex] = 2 and [tex]y_{2}[/tex] = 6
∴ [tex]m_{1}:m_{2}[/tex] = 1 : 2
Substitute these values in the rules above to find x and y
∴ [tex]x=\frac{(9)(2)+(2)(1)}{1+2}[/tex]
∴ [tex]x=\frac{18+2}{3}[/tex]
∴ [tex]x=\frac{20}{3}[/tex]
∴ x = [tex]6\frac{2}{3}[/tex]
∴ [tex]y=\frac{(3)(2)+(6)(1)}{1+2}[/tex]
∴ [tex]y=\frac{6+6}{3}[/tex]
∴ [tex]y=\frac{12}{3}[/tex]
∴ y = 4
The coordinates of the point that divides the line segment directed
from A to B in the ratio of 1 : 2 are ( [tex]6\frac{2}{3}[/tex] , 4)
Learn more:
You can learn more about point of division in brainly.com/question/5223123
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