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Thread: Analytic Geometry Q6

  1. #1
    Member looi76's Avatar
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    Analytic Geometry Q6

    Question:
    Using slopes, determine if the points lie on a straight line.
    a) $\displaystyle (-1,-4)$ , $\displaystyle (3,8)$ & $\displaystyle (0,-1)$
    b) $\displaystyle (0,5)$ , $\displaystyle (-1,3)$ & $\displaystyle (-3,2)$

    Attempt:

    a) $\displaystyle (-1,-4)$ & $\displaystyle (3,8)$

    $\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{8-(-4)}{3-(-1)} = \frac{12}{4} = 3$

    $\displaystyle (3,8)$ & $\displaystyle (0,-1)$

    $\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-1-8}{0-3} = \frac{-9}{-3} = 3$

    It is a straight line as the slopes are the same.



    b) $\displaystyle (0,5)$ & $\displaystyle (-1,3)$

    $\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{3-5}{-1-0} = 2$

    $\displaystyle (-3,2)$ & $\displaystyle (-1,3)$

    $\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{3-2}{(-1)-3} = \frac{1}{-4} = -\frac{1}{4}$

    It is not a straight line as the slopes don't match.



    are my answers correct?
    Last edited by looi76; Jan 31st 2009 at 02:31 AM. Reason: Correction for question
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  2. #2
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    a) you data is (0,1) but you made the calculation with (0,-1)

    b) your calculation of the second slope is not correct
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  3. #3
    Member looi76's Avatar
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    a) I have corrected the question. Is my answer right?



    b) $\displaystyle (-3,2)$ & $\displaystyle (-1,3)$

    $\displaystyle \color{red}{m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{3-2}{(-1)-3} = \frac{1}{-4} = -\frac{1}{4}}$

    $\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2-3}{-3-1} = \frac{1}{4}$

    It is still not a straight line, am I right?
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  4. #4
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    a) OK

    b) The slope is still not correct ...
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