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co-ordinate geometry .

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Md.Nazrul Islam Rising GMAT Star
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co-ordinate geometry . Post Fri Apr 06, 2012 9:00 pm
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  • Lap #[LAPCOUNT] ([LAPTIME])
    In the xy-plane line L and K intersect at the point (16/5,12/5 ).what is the slope of the line L .

    1)THE product of the slopes of line L and K is -1.

    2) line K pass through the origin .

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    Post Fri Apr 06, 2012 9:18 pm
    Md.Nazrul Islam wrote:
    In the xy-plane line L and K intersect at the point (16/5,12/5 ).what is the slope of the line L .

    1)THE product of the slopes of line L and K is -1.

    2) line K pass through the origin .
    Let us assume that the equation of line L is y = m1x + b1 and that of line K is y = m2x + b2
    Since (16/5, 12/5) is the point of intersection of 2 lines, so this point lies on the lines also.
    So, 12/5 = m1(16/5) + b1 ... Equation 1
    and 12/5 = m2(16/5) + b2 ... Equation 2

    We have to find the value of m1.

    (1) The product of the slopes of line L and K is -1 implies m1 * m2 = -1, which means the two lines L and K are perpendicular lines. But we cannot find the value of m1; NOT sufficient.

    (2) Line K pass through the origin.
    So, 0 = m2(0) + b2 implies b2 = 0
    This means 12/5 = m2(16/5) + 0
    12 = 16 * m2
    m2 = 3/4
    Again we cannot find the value of m1 from here; NOT sufficient.

    Next, combining (1) and (2), m1 * m2 = -1 and m2 = 3/4 implies m1 * (3/4) = -1
    m1 = -4/3; SUFFICIENT.

    The correct answer is C.

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