Question

Find the ratio in which x axis divides the line segment joining the points (2,-3) and (5,6)then find the intersecting point on x axis

Answer 1

Hope this will help YOU to solve the problem

Answer 2

Answer:

The ratio in which x axis divide the line segment AB is 1 : 2 and coordinate of point of intersection on x-axis is ( 5 , 0 )

Step-by-step explanation:

Given: Points are A( 2 , -3 ) and B( 5 , 6 )

To find: Ratio when line AB intersected by x - axis

             intersecting point on x-axis

let the ratio be k : 1 and the point where line AB intersect x-axis be ( x , 0 )

Section formula is given by,

$coordinate\,of\,point=(\frac{m\times x_2+n\times x_1}{m+n},\frac{m\times y_2+n\times y_1}{m+n})$

So we get,

$coordinate\,of\x-axis=(\frac{k\times5+1\times2}{k+1},\frac{k\times6+1\times(-3)}{k+1})$

$(x,0)=(\frac{5k+2}{k+1},\frac{6k-3}{k+1})$

On comparing y-coordinates we get,

$\implies0=\frac{6k-3}{k+1}$

$0=6k-3$

$6k=3$

$k=\frac{3}{6}$

$k=\frac{1}{2}$

$\implies k:1=\frac{1}{2}:1=1:2$

put value of k in x-coordinate to get x-coordinate of x-axis,

$\implies x=\frac{5\times\frac{1}{2}+2}{\frac{1}{2}+1}$

$x=\frac{\frac{5+10}{2}}{\frac{1+2}{2}}$

$x=\frac{\frac{15}{2}}{\frac{3}{2}}$

$x=\frac{15}{3}$

x = 5

Therefore, The ratio in which x axis divide the line segment AB is 1 : 2 and coordinate of point of intersection on x-axis is ( 5 , 0 )