Question

The ratio in which the point P( 1 ,-7) divides the line joining the points (-4,3) and ( 2,-4)
(a)2 : 5 (b) 5 : 2 (c) 5 : 6 (d) 3 : 5

Answer 1

Answer:

the answer is (b) calculations

Answer 2

Given:

P ( 1 , - 7 )  A ( 2 , -4 ) B ( -4 , 3 )

To find :

The ratio in which the point P( 1 ,-7) divides the line joining the points (-4,3) and ( 2,-4) .

Formula to be used:

P = $(\frac{mx_{2} + nx_{1}}{m+n} , \frac{my_{2} + ny_{1}}{m+n} )$

Solution:  

Let,

$x_{1} = 2\\y_{1} = - 4\\x_{2} = -4\\y_{2} = 3$

By using the formula ,

P = $(\frac{mx_{2} + nx_{1}}{m+n} , \frac{my_{2} + ny_{1}}{m+n} )$

P = $(\frac{(-4)m+ 3(n)}{m+n} , \frac{2(m) + (-4)n}{m+n} )$

( 1 , -7 ) = $(\frac{-4m+ 3n}{m+n} , \frac{2m -4n}{m+n} )$

1 = $(\frac{-4m+ 3n}{m+n} )$

m + n = -4m + 3n

m + 4m = 3n - n

5m = 2n

The ratio is 2 : 5 .

Final answer:

The ratio in which the point P( 1 ,-7) divides the line joining the points (-4,3) and ( 2,-4) is 2: 5 .

Thus , the correct option is (a) 2 : 5