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virtus

  • 3 years ago

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

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  1. ash2326
    • 3 years ago
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    @virtus Are you here?

  2. virtus
    • 3 years ago
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    yes!

  3. ash2326
    • 3 years ago
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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?

  4. virtus
    • 3 years ago
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    sure, thanks ash2326

  5. waterineyes
    • 3 years ago
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    Can I give the formula??

  6. ash2326
    • 3 years ago
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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?

  7. waterineyes
    • 3 years ago
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    Go ahead @ash2326 ..

  8. ash2326
    • 3 years ago
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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?

  9. virtus
    • 3 years ago
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    yes

  10. ash2326
    • 3 years ago
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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?

  11. virtus
    • 3 years ago
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    POI

  12. ash2326
    • 3 years ago
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    POI???

  13. virtus
    • 3 years ago
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    find the Point Of Intersection

  14. waterineyes
    • 3 years ago
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    Ha ha ha ha..

  15. ash2326
    • 3 years ago
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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?

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

  17. virtus
    • 3 years ago
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    oh wait do we know what C is ?

  18. ash2326
    • 3 years ago
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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)

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

  20. ash2326
    • 3 years ago
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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 :)

  21. virtus
    • 3 years ago
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    oh silly me

  22. ash2326
    • 3 years ago
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    No problem, :D find it again?

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

  24. ash2326
    • 3 years ago
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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

  25. virtus
    • 3 years ago
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    D (-1,2)

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

  27. ash2326
    • 3 years ago
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    That will be the perpendicular distance:D

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

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

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

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

  32. dpaInc
    • 3 years ago
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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.

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