Assertion (A): The point (–4, 6) divides the line segment joining A(–6, 10) and B(–7, 4) in the ratio 2 : 9.

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Solution

Q.
Assertion (A): The point (–4, 6) divides the line segment joining A(–6, 10) and B(–7, 4) in the ratio 2 : 9.

Reason (R): The coordinates of the point P(x,y) which divides the line segment joining $A (x_{1}, y_{1}) a n d B (x_{2}, y_{2}) i n t e r n a l l y i n t h e r a t i o m_{1} : m_{2} a r e :$

$(\frac{m_{1} x_{2} + m_{2} x_{1}}{m_{1} + m_{2}}, \frac{m_{1} y_{2} + m_{2} y_{1}}{m_{1} + m_{2}})$

1 Both A and R are true, and R is the correct explanation of A

2 Both A and R are true, but R is not the correct explanation of A

3 A is true, but R is false.

4 A is false, but R is true

Ans.
(4)

Let point P(x,y) divide AB in the ratio 2 : 9.

Using section formula:

$x = \frac{2 (- 7) + 9 (- 6)}{2 + 9} = \frac{- 14 - 54}{11} = - \frac{68}{11} y = \frac{2 (4) + 9 (10)}{2 + 9} = \frac{8 + 90}{11} = \frac{98}{11} T h u s, C o o r d i n a t e s o f p o i n t P a r e (- \frac{68}{11}, \frac{98}{11}) . B u t t h e a s s e r t i o n c l a i m s P i s (- 4, 6), w h i c h i s i n c o r r e c t .$

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