In what ratio does the x-axis divide the join of A(2, −3) and B(5, 6)?


In what ratio does the x-axis divide the join of A(2, −3) and B(5, 6)?

(a) 2 : 3
(b) 3 : 5
(c) 1 : 2
(d) 2 : 1


(c) 1 : 2

Let $A B$ be divided by the $x$ axis in the ratio $k: 1$ at the point $P$.

Then, by section formula, the coordinates of are

$P\left(\frac{5 k+2}{k+1}, \frac{6 k-3}{k+1}\right)$

But P lies on the x axis: so, its ordinate is 0.

$\frac{6 k-3}{k+1}=0$

$\Rightarrow 6 k-3=0$

$\Rightarrow 6 k=3$

$\Rightarrow k=\frac{1}{2}$

Hence, the required ratio is $\frac{1}{2}: 1$, which is same as $1: 2$.


Leave a comment


Click here to get exam-ready with eSaral

For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.

Download Now