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virtus

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

  • one year ago
  • one year ago

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  1. ash2326
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    @virtus Are you here?

    • one year ago
  2. virtus
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    yes!

    • one year ago
  3. ash2326
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    @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?

    • one year ago
  4. virtus
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    sure, thanks ash2326

    • one year ago
  5. waterineyes
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    Can I give the formula??

    • one year ago
  6. ash2326
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    Thanks virtus, let's begin. I recommend that you understand the problem, you'll remember it always. What do you want?

    • one year ago
  7. waterineyes
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    Go ahead @ash2326 ..

    • one year ago
  8. ash2326
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    |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?

    • one year ago
  9. virtus
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    yes

    • one year ago
  10. ash2326
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    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?

    • one year ago
  11. virtus
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    POI

    • one year ago
  12. ash2326
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    POI???

    • one year ago
  13. virtus
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    find the Point Of Intersection

    • one year ago
  14. waterineyes
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    Ha ha ha ha..

    • one year ago
  15. ash2326
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    Yeah:) @virtus For that we need to find the equation of the line CD, do you have any idea how to do that?

    • one year ago
  16. virtus
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    well you know what point C is and the gradient of line CD would be -1/ gradient of line AB

    • one year ago
  17. virtus
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    oh wait do we know what C is ?

    • one year ago
  18. ash2326
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    Awesome:D Could you do that? We have AB as \(x+3y-5=0\) Yeah we know C as (0, 5)

    • one year ago
  19. virtus
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    x+3y-15=0

    • one year ago
  20. ash2326
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    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 :)

    • one year ago
  21. virtus
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    oh silly me

    • one year ago
  22. ash2326
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    No problem, :D find it again?

    • one year ago
  23. virtus
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    y-5 =3(x-0) y=3x +5 3x-y+5=0

    • one year ago
  24. ash2326
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    Correct:D Now find the intersection of the line (3x-y+5=0) and (x+3y-5=0) this will give us D

    • one year ago
  25. virtus
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    D (-1,2)

    • one year ago
  26. ash2326
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    Great work:D now find the distance between (0, 5) and (-1, 2) using distance formula.

    • one year ago
  27. ash2326
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    That will be the perpendicular distance:D

    • one year ago
  28. virtus
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    ngawwwwwww! I SEE!!!! so that's how you do it ;) oh btw i got square root 10

    • one year ago
  29. ash2326
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    Yeah, that's correct:D Great work btw:D

    • one year ago
  30. virtus
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    thanks so much for your invaluble help @ash2326 :D

    • one year ago
  31. ash2326
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    @virtus you did all the work. I just guided you:D You are a good student:D

    • one year ago
  32. dpaInc
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    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.

    • one year ago
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