Question

Line segment AB has endpoints A(9, 3) and B(2, 6). Find the coordinates of the point that divides the line segment directed from A to B in the ratio of 1:2.

Answer 1

The coordinates of the point that divides the line segment directed

from A to B in the ratio of 1 : 2 are ( $6\frac{2}{3}$ , 4)

Step-by-step explanation:

If point (x , y) divides a line segment whose endpoints are $(x_{1},y_{1})$

and $(x_{2},y_{2})$ at ratio $m_{1}:m_{2}$ from $(x_{1},y_{1})$ , then

• $x=\frac{x_{1}m_{2}+x_{2}m_{1}}{m_{1}+m_{2}}$

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

∵ 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

∴ $x_{1}$ = 9 and $y_{1}$ = 3

∴ $x_{2}$ = 2 and $y_{2}$ = 6

∴ $m_{1}:m_{2}$ = 1 : 2

Substitute these values in the rules above to find x and y

∴ $x=\frac{(9)(2)+(2)(1)}{1+2}$

∴ $x=\frac{18+2}{3}$

∴ $x=\frac{20}{3}$

∴ x = $6\frac{2}{3}$

∴ $y=\frac{(3)(2)+(6)(1)}{1+2}$

∴ $y=\frac{6+6}{3}$

∴ $y=\frac{12}{3}$

∴ y = 4

The coordinates of the point that divides the line segment directed

from A to B in the ratio of 1 : 2 are ( $6\frac{2}{3}$ , 4)

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Answer 2

Answer:

20/3, 4

Step-by-step explanation: