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Mathematics 14 Online
OpenStudy (anonymous):

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

OpenStudy (ash2326):

@virtus Are you here?

OpenStudy (anonymous):

yes!

OpenStudy (ash2326):

@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?

OpenStudy (anonymous):

sure, thanks ash2326

OpenStudy (anonymous):

Can I give the formula??

OpenStudy (ash2326):

Thanks virtus, let's begin. I recommend that you understand the problem, you'll remember it always. What do you want?

OpenStudy (anonymous):

Go ahead @ash2326 ..

OpenStudy (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?

OpenStudy (anonymous):

yes

OpenStudy (ash2326):

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?

OpenStudy (anonymous):

POI

OpenStudy (ash2326):

POI???

OpenStudy (anonymous):

find the Point Of Intersection

OpenStudy (anonymous):

Ha ha ha ha..

OpenStudy (ash2326):

Yeah:) @virtus For that we need to find the equation of the line CD, do you have any idea how to do that?

OpenStudy (anonymous):

well you know what point C is and the gradient of line CD would be -1/ gradient of line AB

OpenStudy (anonymous):

oh wait do we know what C is ?

OpenStudy (ash2326):

Awesome:D Could you do that? We have AB as \(x+3y-5=0\) Yeah we know C as (0, 5)

OpenStudy (anonymous):

x+3y-15=0

OpenStudy (ash2326):

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 :)

OpenStudy (anonymous):

oh silly me

OpenStudy (ash2326):

No problem, :D find it again?

OpenStudy (anonymous):

y-5 =3(x-0) y=3x +5 3x-y+5=0

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