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anonymous

  • 4 years ago

Find the distance from (2,-1) to the line y=2x+3. The answer is 8/5*root5 by the way, but I want to know how to solve. I used distance formula. sqrt ( (x-2)^2 + (y+1)^2) sqrt ( (x-2)^2 + (2x+3+1)^2) sqrt ( (x-2)^2 + (2x+4)^2) sqrt (5x^2 + 12x + 20) When I enter this on my calculator to solve for x, it cannot do it. What should I do next?

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  1. anonymous
    • 4 years ago
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    you don't use X

  2. precal
    • 4 years ago
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    What kind of calculator are you using? Are you using the solve feature?

  3. anonymous
    • 4 years ago
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    Yes I am usin the solve feature.

  4. precal
    • 4 years ago
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    Why don't you use graph paper instead?

  5. anonymous
    • 4 years ago
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    I have to use algebraic methods and show my work.

  6. precal
    • 4 years ago
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    graphing on graph paper is a way to show your work

  7. anonymous
    • 4 years ago
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    Is there a way to answer the problem algebraically?

  8. anonymous
    • 4 years ago
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    Well, the line to the other linen willl be perpendicular to it

  9. anonymous
    • 4 years ago
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    Assuming you want the shortest distance

  10. precal
    • 4 years ago
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    using graph paper is a valid method, then you can count the number of units

  11. anonymous
    • 4 years ago
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    Find the equation of a line perpendicular to y=2x+3 and use the distance formula on the intersection

  12. precal
    • 4 years ago
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    You could use a point from the equation. I would graph it to decide what point to use. You need two ponts for the distance formula

  13. Mertsj
    • 4 years ago
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    Have you studied the formula for finding the perpendicular to a line through a point?

  14. anonymous
    • 4 years ago
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    Well, I'm in Calculus right now, but I don't know how to continue this problem.

  15. precal
    • 4 years ago
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    Yep calculus would study that Do the normal line

  16. anonymous
    • 4 years ago
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    Wouldn't the normal slope be -1/2 ?

  17. anonymous
    • 4 years ago
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    -1/2*

  18. anonymous
    • 4 years ago
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    \[y+1=\frac{-1}{2}(x-2)\]

  19. anonymous
    • 4 years ago
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    \[y=-\frac{1}{2}x\]

  20. Mertsj
    • 4 years ago
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    You could put the equation in the form Ax+By=C=0 and use this formula: \[d=\frac{|Am+Bn+C|}{\sqrt{A ^{2}+B ^{2}}}\] The point is (m,n)

  21. anonymous
    • 4 years ago
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    Now set 2x+3=-(1/2)x to find the intersection, then use the distance formula

  22. anonymous
    • 4 years ago
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    x = -6/5

  23. anonymous
    • 4 years ago
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    Get y now, and use this point in your distance formula

  24. precal
    • 4 years ago
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    Mertsj what formula did you post? Do you know the name of it? Just curious

  25. Mertsj
    • 4 years ago
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    Perpendicular distance from a Point to a Line

  26. precal
    • 4 years ago
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    ok I have not seen that one before. Good to know

  27. anonymous
    • 4 years ago
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    Okay I now have two methods of approaching this problem. Thank you all for helping me. :)

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