Question

the length of perpendicular from (7,-2) to the line x+2y-5=0 is

Answer 1

Answer:

5 is the answer

Step-by-step explanation:

gut feeling

Answer 2

Answer:

The answer is  $\dfrac{2}{\sqrt 5}=\dfrac{2\sqrt 5}{5}$

Step-by-step explanation:

Concept:  

Perpendicular distance of a point $(x_1,y_1)$ from the line $ax+by+c=0$ is

                              $\boxed{\dfrac{|ax_1+y_1+c|}{\sqrt{a^2+b^2}}}$

Therefore length of perpendicular from $(7,-2)$ to the line $x+2y-5=0$ is

                           $=\dfrac{|7+2(-2)-5|}{\sqrt{1^2+2^2}}=\dfrac{|7-4-5|}{\sqrt 5}=\dfrac{|-2|}{\sqrt 5}=\dfrac{2}{\sqrt 5}=\dfrac{2\sqrt 5}{5}$