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virtus
 2 years ago
perpendicular distance from point B(0,5) to the line x+3y5=0
virtus
 2 years ago
perpendicular distance from point B(0,5) to the line x+3y5=0

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ash2326
 2 years ago
Best ResponseYou've already chosen the best response.2@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?

waterineyes
 2 years ago
Best ResponseYou've already chosen the best response.0Can I give the formula??

ash2326
 2 years ago
Best ResponseYou've already chosen the best response.2Thanks virtus, let's begin. I recommend that you understand the problem, you'll remember it always. What do you want?

waterineyes
 2 years ago
Best ResponseYou've already chosen the best response.0Go ahead @ash2326 ..

ash2326
 2 years ago
Best ResponseYou've already chosen the best response.2dw: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?

ash2326
 2 years ago
Best ResponseYou've already chosen the best response.2You 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?

virtus
 2 years ago
Best ResponseYou've already chosen the best response.2find the Point Of Intersection

ash2326
 2 years ago
Best ResponseYou've already chosen the best response.2Yeah:) @virtus For that we need to find the equation of the line CD, do you have any idea how to do that?

virtus
 2 years ago
Best ResponseYou've already chosen the best response.2well you know what point C is and the gradient of line CD would be 1/ gradient of line AB

virtus
 2 years ago
Best ResponseYou've already chosen the best response.2oh wait do we know what C is ?

ash2326
 2 years ago
Best ResponseYou've already chosen the best response.2Awesome:D Could you do that? We have AB as \(x+3y5=0\) Yeah we know C as (0, 5)

ash2326
 2 years ago
Best ResponseYou've already chosen the best response.2Oops, 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 :)

ash2326
 2 years ago
Best ResponseYou've already chosen the best response.2No problem, :D find it again?

virtus
 2 years ago
Best ResponseYou've already chosen the best response.2y5 =3(x0) y=3x +5 3xy+5=0

ash2326
 2 years ago
Best ResponseYou've already chosen the best response.2Correct:D Now find the intersection of the line (3xy+5=0) and (x+3y5=0) this will give us D

ash2326
 2 years ago
Best ResponseYou've already chosen the best response.2Great work:D now find the distance between (0, 5) and (1, 2) using distance formula.

ash2326
 2 years ago
Best ResponseYou've already chosen the best response.2That will be the perpendicular distance:D

virtus
 2 years ago
Best ResponseYou've already chosen the best response.2ngawwwwwww! I SEE!!!! so that's how you do it ;) oh btw i got square root 10

ash2326
 2 years ago
Best ResponseYou've already chosen the best response.2Yeah, that's correct:D Great work btw:D

virtus
 2 years ago
Best ResponseYou've already chosen the best response.2thanks so much for your invaluble help @ash2326 :D

ash2326
 2 years ago
Best ResponseYou've already chosen the best response.2@virtus you did all the work. I just guided you:D You are a good student:D

dpaInc
 2 years ago
Best ResponseYou've already chosen the best response.0you 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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