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Math Help - Stuck on this question.

  1. #1
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    Stuck on this question.

    I just can't work it out, can someone please post how to solve it:

    If line1(l1) is a line through (3,-2) and (6,1) and line2(l2) is a line through (2,0) which makes an angle at 45 degree with the positive x-axis then are l1 and l2 parallel?

    Thanks in advance.
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  2. #2
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    Quote Originally Posted by JohnLord123 View Post
    I just can't work it out, can someone please post how to solve it:

    If line1(l1) is a line through (3,-2) and (6,1) and line2(l2) is a line through (2,0) which makes an angle at 45 degree with the positive x-axis then are l1 and l2 parallel?

    Thanks in advance.
    Join (3,-2) to (6,1).
    Draw a right-angled triangle using the point (6,-2).

    \theta is the acute angle at the (3,-2) vertex.

    The perpendicular sides of the triangle have lengths 6-3=3 and 1-(-2)=3.

    (6,1) is 3 units above (6,-2).

    tan\theta=1

    \theta=45^o
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  3. #3
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    Or (pretty much the same thing): \frac{y_2- y_1}{x_2- x_1}= \frac{1- (-2)}{6- 3}= \frac{3}{3}= 1. Since that is equal to the tan(45), the two lines make the same angle with the x-axis and so are parallel.
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