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Math Help - Co-ordinate Geometery urgent help needed

  1. #1
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    Co-ordinate Geometery urgent help needed

    A, B, C and D are (-7,4), (3,-1), (6,1) and (k,-15) respectively.

    1] Find the gradient of AB
    2] Find the equation of AB and simplify the answer
    3] Find the length of AB
    4] The point E is the mid-point of AB. Find the co-ordinates of E.
    5] CD is perpendicular to AB. Find the value of k in D.

    For question 1 I used y2-y1 over x2-x1 to get the gradient which I think is -6,

    For question 2 I then used formula of a line and continued:

    y - y1 = m (x - x1)
    y - 4 = -6 (x + 7)
    y - 4 = -6x - 42
    y + 6x + 38 = 0

    For question 3 I worked the length of AB to be:

    √ (x2-x1) + (y2-y1)
    √ (3 + 7) + (-1 + 7)
    √ 10 + 6 [100 = 36]
    AB = √136

    I'm really concerned this is wrong and I don't know how to do the rest of the question. Can someone please help me?
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  2. #2
    Member TheMasterMind's Avatar
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    Quote Originally Posted by db5vry View Post
    A, B, C and D are (-7,4), (3,-1), (6,1) and (k,-15) respectively.

    1] Find the gradient of AB
    2] Find the equation of AB and simplify the answer
    3] Find the length of AB
    4] The point E is the mid-point of AB. Find the co-ordinates of E.
    5] CD is perpendicular to AB. Find the value of k in D.

    For question 1 I used y2-y1 over x2-x1 to get the gradient which I think is -6,

    For question 2 I then used formula of a line and continued:

    y - y1 = m (x - x1)
    y - 4 = -6 (x + 7)
    y - 4 = -6x - 42
    y + 6x + 38 = 0

    For question 3 I worked the length of AB to be:

    √ (x2-x1) + (y2-y1)
    √ (3 + 7) + (-1 + 7)
    √ 10 + 6 [100 = 36]
    AB = √136

    I'm really concerned this is wrong and I don't know how to do the rest of the question. Can someone please help me?
    1/ is wrong,

    \frac{y_2-y_1}{x_2-x_1}= \frac{-1-4}{3+7}

    \frac{-5}{10} =-\frac{1}{2}

    2/ i get -\frac{1}{2}x+\frac{1}{2} you already have the slope which is -\frac{1}{2} plug in the other numbers to y=-\frac{1}{2}x+b and solve for b

    3/ the value of y1 is 4 and you used 7 which is wrong
    answer should be \sqrt{125}= 11.18

    4/

    M= (\frac{x_1+x_2}{2} + \frac{y_1+y_2}{2})= (\frac{-7+3}{2} + \frac{4-1}{2})

    =(\frac{-4}{2} + \frac{3}{2}) =(-2,1/2)
    Last edited by TheMasterMind; January 7th 2009 at 04:58 PM.
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