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anonymous

  • 4 years ago

Find the distance from the point (2,-1) to the line y = 2x + 3

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  1. amistre64
    • 4 years ago
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    y = -1/2 x +(2)/2 - 1 y = -1/2 x seems to be the line with the point on it system of equation to find the intersection then distance it from point to point

  2. amistre64
    • 4 years ago
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    2x+3 = -1/2 x 5/2 x = -3 x = -3/(5/2) = -6/5 maybe :)

  3. amistre64
    • 4 years ago
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    -1/2 * -6/5 = 6/10 = 3/5 then 2(-6/5) + 3 = -12/5 + 15/5 = 3/5 so thats a match

  4. anonymous
    • 4 years ago
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    My correct answer says : 8/5 * sqrt(5), could you help me to get there?

  5. amistre64
    • 4 years ago
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    (10/5, -5/5) - (-6/5 , 10/5) --------------- (16/5)^2 + (-15/5)^2 sqrt(16^2+15^2)/5 should be it then

  6. amistre64
    • 4 years ago
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    seeing how i thought my first explanation was suffieicnt; youll have to address where it is your following goes amiss at

  7. amistre64
    • 4 years ago
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    other than typos :)

  8. amistre64
    • 4 years ago
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    |dw:1327864212303:dw|

  9. amistre64
    • 4 years ago
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    y = 2x + 3 needs a perp line to it; perp line is just flip and negate the slope 2 flips to -1/2 y = -1/2 x + b ; use (2,-1) to calibrate 2 = -1(-1)/2 + c 2 = 2 + c ; c = 0 y = -1/2 x is equation of line perp to and containing (2,-1)

  10. amistre64
    • 4 years ago
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    if we know where the lines meet, we have a point of reference to measure distance with ...|dw:1327864376411:dw|

  11. amistre64
    • 4 years ago
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    y = 2x + 3 -( y = -1/2 x) ------------- 0 = 5/2 x + 3 ; when x = -3/5

  12. amistre64
    • 4 years ago
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    y = -1/2 * -3/5 = 3/10 therefore, point of intersection is: (-3/2 , 3/10) looks better

  13. amistre64
    • 4 years ago
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    (-3/5 , 3/10) that is

  14. amistre64
    • 4 years ago
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    |dw:1327864617337:dw|

  15. amistre64
    • 4 years ago
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    use distance formula for distance

  16. amistre64
    • 4 years ago
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    ugh!!, lost my x ... 5/2 * -2/5 * 3 = -6/5 0 = 5*-6/2*5 + 3 0 = -30/10 + 3 = -3+3 x = -6/5 ....

  17. amistre64
    • 4 years ago
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    y = -1/2*-6/5 = 6/10 = 3/5 (-6/5, 3/5) is the point of intersection .....

  18. amistre64
    • 4 years ago
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    \[d=\sqrt{(2-\frac{-6}{5})^2+(-1-\frac{3}{5})^2}\] \[d=\sqrt{(\frac{10+6}{5})^2+(\frac{-5-3}{5})^2}\] \[d=\sqrt{(\frac{16}{5})^2+(\frac{-8}{5})^2}\] \[d=\frac{\sqrt{16^2+8^2}}{5}\]

  19. amistre64
    • 4 years ago
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    that simplifies to 8sqrt(5)/5

  20. anonymous
    • 4 years ago
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    |dw:1327864993315:dw|

  21. anonymous
    • 4 years ago
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    that is what we found?

  22. amistre64
    • 4 years ago
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    yes

  23. anonymous
    • 4 years ago
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    Why doesn't using the pythagorean theorem work here?

  24. amistre64
    • 4 years ago
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    it does, but first you need to know 2 points. the given point (2,-1) and the intersection of the perped lines

  25. amistre64
    • 4 years ago
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    once you know the 2 points, the distance formula IS the pythag thrm

  26. anonymous
    • 4 years ago
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    " the intersection of the perped lines" confused me, I am really stumped because, I still don't understand why we can't just draw the right triangle from the y axis to the point 2,-1

  27. amistre64
    • 4 years ago
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    because you dont want the distance from the y axis, you want the distance to the line and the point; that distance is defined as the shortest distance between the line and the point. which just so happens to make a 90degree angle when it hits|dw:1327865470057:dw|

  28. amistre64
    • 4 years ago
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    teh y axis has nothing to do with it at all

  29. anonymous
    • 4 years ago
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    OH, THE POINT OF PERPENDICULAR(ness)? to the point 2,-1?

  30. amistre64
    • 4 years ago
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    yes

  31. anonymous
    • 4 years ago
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    which is the part where we found the perp. point? that is the next step correct?

  32. anonymous
    • 4 years ago
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    we do the negative inversse, OH, then we go from the point 2,-1 towards the other line, using the perpendicular slope, is that right?

  33. anonymous
    • 4 years ago
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    until there is an intersection

  34. amistre64
    • 4 years ago
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    yep

  35. anonymous
    • 4 years ago
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    is there an equation to find that point?

  36. amistre64
    • 4 years ago
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    its solving a system of equations; y = 2x + 3 y = -1/2x we can sub, eliminate, or any other method to solve the sytem

  37. amistre64
    • 4 years ago
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    it turns out that i used elimination and came up with those fractions

  38. amistre64
    • 4 years ago
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    y = -1/2 x -2y = x, sub in top y = 2(-2y) + 3 y = -4y + 3 5y = 3 y = 3/5

  39. amistre64
    • 4 years ago
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    knowing y, solve for x

  40. amistre64
    • 4 years ago
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    3/5 = -1/2 x -2*3/5 = x -6/5 = x

  41. amistre64
    • 4 years ago
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    those x and y parts are the point of intersection

  42. anonymous
    • 4 years ago
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    ahhh, i understand now... now i use the distance formula between the points (-6/5, 3/5) and (2,-1) Hey, i'd like to thank you for spending about an hour of your time to help me understand this, i appreciate it, much kudos to you.

  43. amistre64
    • 4 years ago
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    youre welcome :)

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