Question

Find the The ratio in which the x-axis divides the line segment joining the points A(a1,b1) and B(a2,b2)

Answer 1

Take ratio as k:1 and apply section formula where point is (x , 0)

Answer 2

Answer:

The ratio in which the x-axis divide the line segment joining the points $A(a_1,b_1)\text{ and }B(a_2,b_2)$ is $-b_1:b_2$

Step-by-step explanation:

The ratio in which the x-axis divides the line segment joining the points $A(a_1,b_1)\text{ and }B(a_2,b_2)$

Point at x-axis therefore their y-coordinate must be 0.

Formula: Using section formula

$(x,y)\rightarrow (\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n})$

Let point P divide AB in ratio k:1

$y\rightarrow \dfrac{kb_2+b_1}{k+1}$

Point is on x-axis, Thus, y=0

$\dfrac{kb_2+b_1}{k+1}=0$

$kb_2+b_1=0$

$k=\dfrac{-b_1}{b_2}$

Hence, The ratio in which the x-axis divide the line segment joining the points $A(a_1,b_1)\text{ and }B(a_2,b_2)$ is $-b_1:b_2$