anonymous
  • anonymous
perpendicular distance from point B(0,5) to the line x+3y-5=0
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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ash2326
  • ash2326
@virtus Are you here?
anonymous
  • anonymous
yes!
ash2326
  • 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?

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anonymous
  • anonymous
sure, thanks ash2326
anonymous
  • anonymous
Can I give the formula??
ash2326
  • ash2326
Thanks virtus, let's begin. I recommend that you understand the problem, you'll remember it always. What do you want?
anonymous
  • anonymous
Go ahead @ash2326 ..
ash2326
  • 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?
anonymous
  • anonymous
yes
ash2326
  • 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?
anonymous
  • anonymous
POI
ash2326
  • ash2326
POI???
anonymous
  • anonymous
find the Point Of Intersection
anonymous
  • anonymous
Ha ha ha ha..
ash2326
  • ash2326
Yeah:) @virtus For that we need to find the equation of the line CD, do you have any idea how to do that?
anonymous
  • anonymous
well you know what point C is and the gradient of line CD would be -1/ gradient of line AB
anonymous
  • anonymous
oh wait do we know what C is ?
ash2326
  • ash2326
Awesome:D Could you do that? We have AB as \(x+3y-5=0\) Yeah we know C as (0, 5)
anonymous
  • anonymous
x+3y-15=0
ash2326
  • 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 :)
anonymous
  • anonymous
oh silly me
ash2326
  • ash2326
No problem, :D find it again?
anonymous
  • anonymous
y-5 =3(x-0) y=3x +5 3x-y+5=0
ash2326
  • ash2326
Correct:D Now find the intersection of the line (3x-y+5=0) and (x+3y-5=0) this will give us D
anonymous
  • anonymous
D (-1,2)
ash2326
  • ash2326
Great work:D now find the distance between (0, 5) and (-1, 2) using distance formula.
ash2326
  • ash2326
That will be the perpendicular distance:D
anonymous
  • anonymous
ngawwwwwww! I SEE!!!! so that's how you do it ;) oh btw i got square root 10
ash2326
  • ash2326
Yeah, that's correct:D Great work btw:D
anonymous
  • anonymous
thanks so much for your invaluble help @ash2326 :D
ash2326
  • ash2326
@virtus you did all the work. I just guided you:D You are a good student:D
anonymous
  • anonymous
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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