Question

5. Find the ratio in which the line segment joining A(1,-5) and B(-4,5) is divided by the
x-axis. Also find the coordinates of the point of division.
​

Answer 1

Given

• A line segment AB
• wher A(1,-5) B(-4,5)
• Divided by X axis

To find

• coordinates of the point division

Solution

Here the point of division is on X axis

Therefore

(X,y) = (X,0)

$\sf\:X=\frac{mx_2+nx_1}{m+n}$

&

$\sf\:Y=\frac{my_2+ny_1}{m+n}$

Putting the values

$\sf\:Y=\frac{my_2+ny_1}{m+n}$

$\implies\sf\orange\:Y=\frac{my_2+ny_1}{m+n}$

$\implies\sf\red\:0=\frac{5m-5n}{m+n}$

=>5m=5n

=>m=n

$\implies\sf\:\frac{1}{1}=\frac{m}{n}$

Now for X

$\sf\:X=\frac{mx_2+nx_1}{m+n}$

$\implies\sf\:X=\frac{mx_2+nx_1}{1+1}$

$\implies\sf\:X=\frac{-4+1}{2}$

$\therefore\sf\:X=\frac{-3}{2}$

Hence,the coordinate of division is (-3/2,0)