Question

Find the ratio in which the point ( a ,1) divides the join of A (-5, 4 ) and B (3,-2).
Hence find a.
​

Answer 1

Step-by-step explanation:

Let's assume the point P (1,a) divide the lin segment AB in the ratio k:1.

Then by section formula, we have

1=

Answer 2

$\large\sf\underline{Given}$

• A = ( -5 , 4 )

• B = ( 3 , -2 )

$\large\sf\underline{To\:find}$

• Ratio in which the point ( a , 1 ) divides the line .

• Value of a .

$\large\sf\underline{Solution}$

Using the section formula , if a point ( x , y ) divides the line joining the points ( x1 , y1 ) and ( x2 , y2 ) in the ratio m : n , then

$\small{\underline{\boxed{\mathrm\pink{(x,y)=[\frac{mx2+nx1}{m+n} ,\frac{my2+ny1}{m+n} ]}}}}$

Let point P divides the join of A and B in the ratio m : n , then

$\sf➣\:1=\frac{m(3)+n(-5)}{m+n}$

$\sf➣\:1=\frac{3m-5n}{m+n}$

$\sf➣\:m+n=3m-5n$

$\sf➣\:m-3m=-5n-n$

$\sf➣\:-2m=-6n$

$\sf➣\:2m=6n$

$\sf➣\:\frac{m}{n}=\frac{6}{2}$

$\sf➣\:\frac{m}{n}=\frac{3}{1}$

${\sf{{\pink{➻\:m:n=3:1}}}}$

Now ,

$\sf⟹\:a=\frac{m(-2)+n(4)}{m+n}$

$\sf⟹\:a=\frac{3 \times (-2)+ 1 \times (4)}{3+1}$

$\sf⟹\:a=\frac{-6+4}{4}$

$\sf⟹\:a=\frac{-2}{4}$

${\sf{{\pink{➻\:a=\frac{-1}{2}}}}}$

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${\sf{{\red{AnsweR:}}}}$

Ratio in which the point ( a , 1 ) divides the line = $\small{\underline{\boxed{\mathrm\purple{m:n=3:1}}}}$

Value of a =$\small{\underline{\boxed{\mathrm\pink{\frac{-1}{2}}}}}$

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• Thnku :)