Question 620474
<pre>
There is also a formula for your first problem:

The distance from the point 

(x<sub>1</sub>,y<sub>1</sub>) to the line whose equation is Ax + By + C = 0 

is given by the formula:

d = {{{(Ax[1]+By[1]+C)/sqrt(A^2+B^2)}}}

Your equation is 

y = -2x - 1

which is equivalent to

2x + y + 1 = 0

Compare that to

Ax + By + C = 0

and A=2, B=1, and C=1,  (x<sub>1</sub>,y<sub>1</sub>) = (1,5) 

Substitute in

d = {{{(Ax[1]+By[1]+C)/sqrt(A^2+B^2)}}}

d = {{{((2)(1)+(1)(5)+1)/sqrt(2^2+1^2)}}}

d = {{{(2+5+1)/sqrt(4+1)}}}

d = {{{8/sqrt(5)}}}
d = {{{8/sqrt(5)}}}·{{{sqrt(5)/sqrt(5)}}}

d = {{{8sqrt(5)/5}}} which is approximately 3.5777, as the other tutor found.

Edwin</pre>