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perpendicular distance from point B(0,5) to the line x+3y-5=0

Mathematics
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@virtus Are you here?
yes!
@virtus There maybe a direct formula for this, but I don't remember that. I'll start from the basics. Do you have time for this?

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Other answers:

sure, thanks ash2326
Can I give the formula??
Thanks virtus, let's begin. I recommend that you understand the problem, you'll remember it always. What do you want?
Go ahead @ash2326 ..
|dw:1341645333105:dw| Let AB be our line and C is the point for which we need to find the perpendicular distance. Do you understand the diagram?
yes
You can see that the perpendicular line from the point C is intersecting the line AB at a point. Let it be D If we could find the coordinates of D, then we can easily find the distance. do you have any ideas what should we do?
POI
POI???
find the Point Of Intersection
Ha ha ha ha..
Yeah:) @virtus For that we need to find the equation of the line CD, do you have any idea how to do that?
well you know what point C is and the gradient of line CD would be -1/ gradient of line AB
oh wait do we know what C is ?
Awesome:D Could you do that? We have AB as \(x+3y-5=0\) Yeah we know C as (0, 5)
x+3y-15=0
Oops, You made a mistake I can see that perpendicular line's slope is same as AB, it's to be -1/ slope AB Check again :)
oh silly me
No problem, :D find it again?
y-5 =3(x-0) y=3x +5 3x-y+5=0
Correct:D Now find the intersection of the line (3x-y+5=0) and (x+3y-5=0) this will give us D
D (-1,2)
Great work:D now find the distance between (0, 5) and (-1, 2) using distance formula.
That will be the perpendicular distance:D
ngawwwwwww! I SEE!!!! so that's how you do it ;) oh btw i got square root 10
Yeah, that's correct:D Great work btw:D
thanks so much for your invaluble help @ash2326 :D
@virtus you did all the work. I just guided you:D You are a good student:D
you can also use the formula from analytic geometry that the distance from a given point to a given line in general form \(\large Ax+By+C=0 \) is given by Distance = \(\large \frac{Ax_0+By_0+C}{\pm \sqrt{A^2+B^2}} \) where \(\ (x_0, y_0) \) are the coordinates of the given point.

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