Question

Find the ratio in which the x-axis divides the line segment joining

the points A (3, 6) and B (12, -3)​

Answer 1

$\huge\green\bigstar{SoLuTiOn}$

Step by step explanation:-

Given :-

• The x axis divides line segment of points A (3,6) B (12, -3)

To find :-

Ratio of x axis

Concept to know :-

If the cordinates of $\sf{(x_1, y_1)}$ , $\sf{(x_2,y_2}$ x axis divides the line segment in ratio $\sf\dfrac{-y_1}{y_2}$

Solution:-

So, A (3, 6) and B (12, -3) are the points

$\sf{x_1 = 3}$

$\sf{x_2 = 12}$

$\sf{y_1 = 6}$

$\sf{y_2 = -3}$

So, it divides x axis in ratio $\sf\dfrac{-y_1}{y_2}$

= $\sf\dfrac{-6}{-3}$

= $\sf\dfrac{6}{3}$

= $\sf\dfrac{3\times2}{3}$

= $\sf\dfrac{2}{1}$

So, the x axis divides the line segment in ratio 2:1

___________________

Know more :-

Distance formula :-

$\sf\sqrt{(x_1-x_2)^2 + (y_1-y_2)^2}$

Mid point formula:-

$\sf\dfrac{x_1 +x_2}{2}$, $\sf\dfrac{y_1+y_2}{2}$

Centroid formula:-

$\sf\dfrac{x_1 +x_2+x_3}{3}$, $\sf\dfrac{y_1+y_2+y_3}{3}$

Section formula for Internal division

$\sf\dfrac{mx_2+nx_1}{m+n}$,$\sf\dfrac{my_2+ny_1}{m+n}$

Section formula for External division

$\sf\dfrac{mx_2-nx_1}{m-n}$,$\sf\dfrac{my_2-ny_1}{m-n}$