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  • Perplex
    IB Math AAHL
    /
    Cartesian plane & lines
    /

    Problem Bank

    [Maximum mark: 23]

    The lines ​x−3y=5​ and ​−3x−y=5​ intersect at ​P. A third straight line, ​L, passes through the origin and has slope ​m. ​L​ intersects ​x−3y=5​ at ​R, and ​−3x−y=5​ at ​Q. The three lines are drawn in the following diagram.

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    1. Show that ​x−3y=5​ is perpendicular to ​−3x−y=5.

      [3]
    2. Find the coordinates of ​P.

      [3]
    3. Give expressions, in terms of the slope ​m​ of ​L, for the lengths

      1. ​[PQ]​

        [5]
      2. ​[PR]​

        [5]

    It is given that area of triangle ​△PQR​ is ​845​units2, and that ​−3<m<31​.

    1. Find the possible value(s) of ​m.

      [7]

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