Find the co-ordinates of the point dividing the joining of line segment $A (1, - 2)$ and $B (4, 7)$ which divides $A B$ internally in the ratio $1 : 2.$

(2, 1)

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(- 2, - 3)

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(1, 2)

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(2, 3)

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Solution

The correct option is A $(2, 1)$
The given points are $A (1, - 2)$ and $B (4, 7)$ .
We have to find the coordinate of points which divide the line segment internally in the ratio $1 : 2$
Let the point $C$ divides the line segment $A B$ in the ratio $1 : 2$

$W e k n o w t h a t i f a p o i n t C (x, y) d i v i d e s t h e l i n e s e g m e n t A B j o i n i n g t h e p o i n t s A (x_{1}, y_{1}) & B (x_{2}, y_{2}) i n t h e r a t i o m : n t h e n, b y t h e s e c t i o n f o r m u l a,$

$\Rightarrow$ $C = (\frac{m x_{2} + n x_{1}}{m + n}, \frac{m y_{2} + n_{1}}{m + n})$

$= (\frac{(1) (4) + (2) (1)}{1 + 2}, \frac{(1) (7) + (2) (- 2)}{1 + 2})$

$= (\frac{6}{3}, \frac{3}{3})$

$= (2, 1)$

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