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 $\frac{5}{4}$

$x_1{y}_1$ $x_2{y}_2$

$(3,3)$ $(7,6)$

A B

equation of line

$\Rightarrow y-y_1=m(x-x_1)$

$\Rightarrow y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

$\Rightarrow y-3=\frac{6-3}{7-3}(x-3)$

$\Rightarrow y-3=\frac{3}{4}(x-3)$

$\Rightarrow 4y-12=3x-9$

$\Rightarrow 3x-4y+3=0$

$\Rightarrow 3x-4y=-3$

if x = ,y = 3/4

y = 0, x = -1

sum $=\sqrt{(1{)}^2+(\frac{3}{4}{)}^2}$

$=\sqrt{1+\frac{9}{16}}$

$=\sqrt{\frac{25}{16}}$

$=\frac{5}{4}$