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anonymous

  • 5 years ago

Find the distance from the point of intersection of the lines 2x+3y=10 and 3x-y=4 to the line 5x-6y=1

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  1. anonymous
    • 5 years ago
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    First find the point set both your equations equal and solve for (x,y) (you could probably even get it by guessing) Then use the distance formula from a point to a line

  2. anonymous
    • 5 years ago
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    The point is 2,2 but I think I'm using the formula for the distance from a point to a line incorrectly... Could you show me how you'd do it?

  3. anonymous
    • 5 years ago
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    Okay, the point is (2,2) and the line is 5x-6y=1 So the formula you can use is just \[\sqrt{ax+by+c} \div \sqrt{a ^{2}}+b ^{2}\] Where the point is (x,y) and the line is ax+by+c=0

  4. anonymous
    • 5 years ago
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    oops.. the ax by and c terms chould all be squared under the root

  5. anonymous
    • 5 years ago
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    actually looking again.. they aren't squared. the first formula is right

  6. anonymous
    • 5 years ago
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    (without the square root)

  7. anonymous
    • 5 years ago
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    yeah That's the formula I have

  8. anonymous
    • 5 years ago
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    so the equation is actually just |ax +by+c| / sqrt(a^2 + b^2 )

  9. anonymous
    • 5 years ago
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    But I'm supposed to use the absolute value, right?

  10. anonymous
    • 5 years ago
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    yeah

  11. anonymous
    • 5 years ago
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    and that's what I think was making me do the question wrong

  12. anonymous
    • 5 years ago
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    so it should be 3 right?

  13. anonymous
    • 5 years ago
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    not -3

  14. anonymous
    • 5 years ago
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    Yeah, but the answer is 0.38

  15. anonymous
    • 5 years ago
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    So does the absolute value apply to the denominator too?

  16. anonymous
    • 5 years ago
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    Well both terms are squared so it won't matter for the bottom

  17. anonymous
    • 5 years ago
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    So... The bottom should be ... \[\sqrt{61}\] right?

  18. anonymous
    • 5 years ago
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    yeah

  19. anonymous
    • 5 years ago
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    Hallelujah the right answer! Finally :) Thanks for your help :)

  20. anonymous
    • 5 years ago
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    awwyeah :)

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