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Math Help - Analytic Geometry Q7

  1. #1
    Member looi76's Avatar
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    Analytic Geometry Q7

    Question:
    Determine if the lines passing through the given pairs of points are parallel, perpendicular or intersect obliquely.

    (a) (1,-1) , (-4,-4) and (1,1) , (4,-4)
    (b) (-6,-4) , (22,8) and (-5,7) , (7,8)

    Attempt:

    (a)
    Slope of : (1,-1) , (-4,-4)

    m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-4-(-1)}{-4-1} = \frac{3}{5}


    Slope of : (1,1) , (4,-4)

    m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-4-1}{4-1} = -\frac{5}{3}


    The lines are perpendicular to each other. We can prove it by using m_1 \times m_2 = -1.


    (b)
    Slope of : (-6,-4) , (22,8)

    m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{8-(-4)}{22 - (-6)} = \frac{3}{7}


    Slope of : (-5,7) , (7,8)

    m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{8-7}{7-(-5)} = \frac{1}{12}

    It is an intersect obliquely.


    Are my answers correct?
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  2. #2
    MHF Contributor
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    Why do you doubt? Did you make any errors deliberately?

    You seem to have this unit. Move on to the next one.

    By the way, very clean and very readable. Keep up the good notation!
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  3. #3
    Member looi76's Avatar
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    Quote Originally Posted by TKHunny View Post
    Why do you doubt? Did you make any errors deliberately?

    You seem to have this unit. Move on to the next one.

    By the way, very clean and very readable. Keep up the good notation!
    Hi TKHunny, Thanks!

    The problem is that I didn't attend the class. I only have the exercises with No Working and No Final Answer.
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  4. #4
    Moo
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    Quote Originally Posted by looi76 View Post
    Hi TKHunny, Thanks!

    The problem is that I didn't attend the class. I only have the exercises with No Working and No Final Answer.
    Well, if you have some doubt, make a sketch and see if your answer looks plausible
    Especially in analytical geometry, it's easy to check.

    If you want a software to draw points and lines, use Geogebra, it's pretty good !
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