Question

In what ratio does the x- axis divide the line segment joining A(5,6) and B (2,-8)?​

Answer 1

Answer:

The x axis divides line joining A and B internally in the ratio 3:4

Step-by-step explanation:

Concept:

The co ordinates of the point which divides the line segment joining $(x_1,y_1)$ and $(x_2,y_2)$ internally in the ratio m:n is

$\bf(\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n})$

Let P be the point on x axis which divides line joining A(5,6) and B(2,-8) internally in the ratio m:n

Then, the coordinates P is

$(\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n})$

$(\frac{m(2)+n(5)}{m+n},\frac{m(-8)+n(6)}{m+n})$

$(\frac{2m+5n}{m+n},\frac{-8m+6n}{m+n})$

since P lies on x axis, y coordinate of P is 0

$\frac{-8m+6n}{m+n}=0$

$-8m+6n=0$

$8m=6n$

$\frac{m}{n}=\frac{6}{8}$

$\frac{m}{n}=\frac{3}{4}$

$\therefore$ The x axis divides line joining A and B internally in the ratio 3:4