Question

If the coordinates of the points A and B be (3, 3) and (7, 6), then the length of the portion of the line AB intercepted between the axes is

• A. $\frac{5}{4}$
• B. $\frac{\sqrt{10}}{4}$
• C. $\frac{\sqrt{13}}{3}$
• D. None of these

Answer 1

The correct option is A $\frac{5}{4}$

Equation of line AB is $Y-3=\frac{6-3}{7-3}(x-3)$
$\Rightarrow 3x-4y+3=0\Rightarrow \frac{x}{-1}+\frac{y}{\frac{3}{4}}=1$
Hence required length is $\sqrt{(-1{)}^2+{\left(\frac{3}{4}\right)}^2}=\frac{5}{4}$ .