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    Just need a little clearing up:

    I have done the following question but part c I got a little confused about because I done a different method and ended up with the wrong answer even though that same method has worked for other questions - and I am just a little worried because I thhought that regardless of what method you use you should still get the same answer. So I am hoping that I have just got confused over a negative sign or something!

    The points A and B have coordinates (4,6) and (12,2) respectively.

    The straight line l1 passes through A and B.

    a) Find an equation for l1 in the form ax + by = c, where a, b and c are integers.

    The straight line l2 passes through the origin and has gradient -4.

    b) Write down an equation for l2.

    The lines l1 and l2 intercept at the point C.

    c) Find the exact coordinates of the mid-point of AC.


    So for part c:

    I got the l1 has an equation of : x + 2y - 16 and l2 has an equation of: y = -4x

    Anyway - instead of spotting the easier method of substituting l1 into l2 I equated the two equations together to make:

    -4x = -1/2x +8

    7/2 x = 8

    x = 16/7

    Therefore y = - 64/7

    so when I used thses coordinates I got the wrong midpoint.

    The answers for the c using the substituiton method should be :

    x = -16/7

    y = 64/7

    and then using these coordinates I get the right midpoint

    Anyway - basically I know I musta gone wrong somewhere with my original method but I just cant see where - because as far as I am concerned it shouldnt matter what method I use, even though mine is slighly more complicated - I should still get the right answer??
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    (Original post by christinajane)
    Just need a little clearing up:

    I have done the following question but part c I got a little confused about because I done a different method and ended up with the wrong answer even though that same method has worked for other questions - and I am just a little worried because I thhought that regardless of what method you use you should still get the same answer. So I am hoping that I have just got confused over a negative sign or something!

    The points A and B have coordinates (4,6) and (12,2) respectively.

    The straight line l1 passes through A and B.

    a) Find an equation for l1 in the form ax + by = c, where a, b and c are integers.

    The straight line l2 passes through the origin and has gradient -4.

    b) Write down an equation for l2.

    The lines l1 and l2 intercept at the point C.

    c) Find the exact coordinates of the mid-point of AC.


    So for part c:

    I got the l1 has an equation of : x + 2y - 16 and l2 has an equation of: y = -4x

    Anyway - instead of spotting the easier method of substituting l1 into l2 I equated the two equations together to make:

    -4x = -1/2x +8

    7/2 x = 8

    x = 16/7

    Therefore y = - 64/7

    so when I used thses coordinates I got the wrong midpoint.

    The answers for the c using the substituiton method should be :

    x = -16/7

    y = 64/7

    and then using these coordinates I get the right midpoint

    Anyway - basically I know I musta gone wrong somewhere with my original method but I just cant see where - because as far as I am concerned it shouldnt matter what method I use, even though mine is slighly more complicated - I should still get the right answer??
    I haven't had time to look over but i'm sure drawing a diagram would help clear things up?
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    (Original post by christinajane)
    ...
    7/2 x = 8.

    Where did this line come from?
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    (Original post by christinajane)
    J
    -4x = -1/2x +8

    7/2 x = 8
    You made an error in going from the first quoted line to the second. Have another go.

    Edit: Too slow :sad:
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    (Original post by ghostwalker)
    You made an error in going from the first quoted line to the second. Have another go.

    Edit: Too slow :sad:
    Ahhh yeah!! Thank you - I knew it was gonna be something silly like those pesky negative signs and me not remembering that I have moved something across the = sign!

    Sometimes I just need someone else to look at these things because I just couldnt see it when I went over it again but yeah it should be

    7/2x = -8

    Then it would all work out, even with my slightly more complicaed method.

    Thanks guys!
 
 
 
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