Question

the distance between the line 2x +4=0and x-5=0 is​

Answer 1

$\textbf{Concept used:}$

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

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

$\text{The given equations are}$

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

$\text{It can be written as}$

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

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

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

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

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

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

Answer 2

Answer:

The distance between them is

\bf|\frac{c_1-c_2}{\sqrt{a^2+b^2}}|∣

a

2

+b

2

c

1

−c

2

∣

=|\frac{2+5}{\sqrt{1^2+0^2}}|=∣

1

2

+0

2

2+5

∣

=|\frac{7}{1}|=∣

1

7

∣

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