Login/Sign Up
Home » In what ratio does the -axis divide the join of and ?
In what ratio does the x-axis divide the join of A(2,-3) and B(5,6) ? \begin{array}{lll}\text { (a) } 2: 3 & \text { (b) } 3: 5 & (\text { c }) 1: 2 & (\text { d) } 2: 1\end{array}
CBSE | Class 10 | Coordinate Geometry | Exercise 16.5 | Maths | RS Aggarwal
In what ratio does the x-axis divide the join of A(2,-3) and B(5,6) ? \begin{array}{lll}\text { (a) } 2: 3 & \text { (b) } 3: 5 & (\text { c }) 1: 2 & (\text { d) } 2: 1\end{array}

The correct option is option (c) 1: 2

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

using  section formula, the coordinates of P are

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

since, lies on the \mathrm{x}-axes so, its ordinate is 0 .

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

\Rightarrow 6 \mathrm{k}-3=0

\begin{aligned} &\Rightarrow 6 \mathrm{k}=3 \\ &\Rightarrow \mathrm{k}=\frac{1}{2} \end{aligned}

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

i

More Material