Q41 / 100 · BITSAT 2023 (Memory Based Paper 1) · Mathematics
If the coordinates of the points $A$ and $B$ be $(3,3)$ and $(7,6)$, then the length of the portion of the line $\mathrm{AB}$ intercepted between the axes is
- Correct answerA$\frac{5}{4}$
- B$\frac{\sqrt{10}}{4}$
- C$\frac{\sqrt{13}}{3}$
- DNone of these
Solution
Equation of line $A B$ is $y-3=\frac{6-3}{7-3}(x-3)$
$\Rightarrow 3 x-4 y+3=0 \Rightarrow \frac{x}{-1}+\frac{y}{3 / 4}=1$
Hence required length is $\sqrt{(-1)^2+\left(\frac{3}{4}\right)^2}=\frac{5}{4}$.
$\Rightarrow 3 x-4 y+3=0 \Rightarrow \frac{x}{-1}+\frac{y}{3 / 4}=1$
Hence required length is $\sqrt{(-1)^2+\left(\frac{3}{4}\right)^2}=\frac{5}{4}$.
Hence, the correct answer is option: 'A'.