Question

The length of the segment of the straight line passing through $(3,3)$ and $(7,6)$ cut off by the coordinate axes is

• A. $\frac{4}{5}$
• B. $\frac{5}{4}$
• C. $\frac{7}{4}$
• D. $\frac{4}{8}$

Answer 1

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

The equation of line through the given points is

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

$⟹4(y-3)=3(x-3)$

$⟹3x-4y+3=0$

Therefore, $x-intercept=(-1,0)andy-intercept=(0,\frac{3}{4})$

Length of segment between the axes $=\sqrt{(0-(-1){)}^2+(\frac{3}{4}-0{)}^2}$

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

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

$=\frac{5}{4}$

Hence the answer is option (B)