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Math Help - Determine point on the line 5x-4y-2=0

  1. #1
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    Determine point on the line 5x-4y-2=0

    The problem

    Determine the point on the line 5x-4y-2=0 where the normal that passes through the point (7,-2) intersects the line.

    Attempt at a solution

    The normal to y= mx+ b has slope -1/m.
    5x- 4y- 2= 0 is the same as 4y= 5x- 2 or y= (5/4)x- 1/2. Its slope is 5/4 so the slope of any normal to it is -4/5.

    What is the equation of the line through (7, -2) with slope -4/5?

    r = (7,-2) + t (-4,5)

    But where do I go from here? Can anyone point me in the right direction?

    Sorry if I'm being a little frustrating, I had pneumonia and missed nearly all the lessons, and I'm really struggling to catch back up.
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  2. #2
    Like a stone-audioslave ADARSH's Avatar
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    What is the equation of the line through (7, -2) with slope -4/5?
    Equation of a line passing through (a,b) having slope "M" is

    (y-b)= M(x-a)

    Use it you are going the correct way
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  3. #3
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    Quote Originally Posted by Random-Hero- View Post
    The problem
    Determine the point on the line 5x-4y-2=0 where the normal that passes through the point (7,-2) intersects the line.
    The normal is 4x+5y-18=0.
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  4. #4
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    So what do I do to find the actual point?
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  5. #5
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    Quote Originally Posted by Random-Hero- View Post
    So what do I do to find the actual point?
    -First you got that equation of normal

    -this intersects with the initial line

    -Solve these two equations to get the point of intersection
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  6. #6
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    After solving the two I got the point (-2,-3)

    Is this correct?
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  7. #7
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    Scratch that, I got (2,2)
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  8. #8
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    The normal is .

    The line is 5x- 4y- 2= 0

    you need to find the point of intersection

    which is done as

    5x-4y-2=0

    5x = 4y+2

    x= \frac{4y+2}{5} <br />
    Put it in equation of normal

    4(\frac{4y+2}{5} + 5y -18 = 0

    \frac{16y+8}{5} = 18-5y

    Multiply both sides by 5

    16y+8 = 90-25y

    41y= 82

    y=2

    Hence x= \frac{8+2}{5}

    x= 2

    Hence point is (2,2)

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  9. #9
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    Thanks all! Really helped me out This is a great community!
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