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

$\frac{5}{4}$

Explanation for the correct option.

Given that, the line passes through $A(3,3)$ and $B(7,6)$,

The equation of the line passing through $\left(x_1,y_1\right),\left(x_2,y_2\right)$ is given by $y-y_1=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)$.

So, the equation of the line $AB$ is:

$\begin{array}{rcl}y-3& =& \frac{6-3}{7-3}(x-3)\\ 3x-4y+3& =& 0\\ \frac{x}{-1}+\frac{y}{{\displaystyle \frac{3}{4}}}& =& 1\end{array}$

Therefore, the required length is $\sqrt{(-1{)}^2+{\left(\frac{3}{4}\right)}^2}=\frac{5}{4}$

Hence, option A is correct.