Question

The ratio in which the x-axis divides the line-segment joining the points A(1,-5)
and B(-4, 5) is :
(A) 2:1
(B) 1:1
(C) 1:2
(D) 3:2
​

Answer 1

$\underline\mathtt{Answer:}$

Option B - 1 : 1 is the ratio

$\underline\mathtt{Explanation:}$

Let the point which the x-axis divides line segment AB be X (x, 0) and the ratio in which it divides be m : n

Let's use the section formula to solve this,

$X(x, 0) = (\frac{m x_{2} + nx_{1}}{m + n} , \frac{m y_{2} + ny_{1}}{m + n} )$

$X (x, 0) = (\frac{m ( - 4)+ n(1)}{m + n} , \frac{m( 5) + n( - 5)}{m + n} )$

The y - coordinates are equal

$0 = \frac{5m - 5n}{m + n}$

$5m -5 n = 0$

$5m = 5n$

$\frac{m}{n} = \frac{1}{1}$

So the ratio m : n = 1 : 1

Have a good afternoon!