Question

16. The distance between the line 2x + 4 = 0 and x-5=0 is(a) 9 units(b) 1 unit(c) 5 units(d) 7 units​

Answer 1

$\textbf{Concept used:}$

$\text{The distance between the parallel lines ax+by+c_1=0 and ax+by+c_2=0 is}$

$\bf|\frac{c_1-c_2}{\sqrt{a^2+b^2}}|$

$\text{The given equations are}$

$2x+4=0\;\text{and}\;x-5=0$

$\text{It can be written as}$

$x+2=0\;\text{and}\;x-5=0$

$\therefore\textbf{The distance between them is}$

$\bf|\frac{c_1-c_2}{\sqrt{a^2+b^2}}|$

$=|\frac{2+5}{\sqrt{1^2+0^2}}|$

$=|\frac{7}{1}|$

$=\bf\;7\;\textbf{units}$

$\therefore\text{option (d) is correct }$