Find the area of the ∆ABC with vertices A(-5, 7), B(-4, -5), a
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    Coordinate Geometry

    Multiple Choice QuestionsShort Answer Type

    231. Find a relation between x and y if the points (x, y); (1, 2) and (7, 0) are collinear.
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    232. Find a relation between x and y if the points (2, 1), (x, y) and (7, 5) are collinear.
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    233. The coordinates of the vertices of ∆ABC are A(4, 1), B(-3, 2) and C(0, k). Given that the area of ABC is 12 unit2, find the value of k.
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    234. Find the area of the ∆ABC with vertices A(-5, 7), B(-4, -5), and C(4, 5).

    Given points are A(-5, 7), B(-4, 5) and C(4, 5).
    Here, we have
    x1 = -5,    y1 = 7
    x2 = -4,    y2 -5
    and    x3 = 4,    y3 = 5
    Area of ∆ABC

    equals 1 half left square bracket straight x subscript 1 left parenthesis straight y subscript 2 minus straight y subscript 3 right parenthesis plus straight x subscript 2 left parenthesis straight y subscript 3 minus straight y subscript 1 right parenthesis plus straight x subscript 3 left parenthesis straight y subscript 1 minus straight y subscript 2 right parenthesis right square bracket equals 1 half left square bracket negative 5 left parenthesis negative 5 minus 5 right parenthesis plus left parenthesis negative 4 right parenthesis left parenthesis 5 minus 7 right parenthesis plus 4 left parenthesis 7 plus 5 right parenthesis right square bracket equals 1 half left square bracket negative 5 space straight x space minus 10 space plus left parenthesis negative 4 space straight x space minus 2 right parenthesis plus 4 space straight x space 12 equals 1 half left square bracket 50 plus 8 plus 48 right square bracket equals 1 half left square bracket 106 right square bracket space equals space 53 space sq. space units.
    Hence area of the ∆ABC = 53 sq. units.

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    235. For what value of k are the points (1, 1), (3, k) and (-1, 4) collinear.
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    236. For what value of p are the points (2, 1), (p, -1) and (-1, 3) collinear.
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    237. Find the area of the rhombus whose vertices taken in order are the points (3, 0), (4, 5), (-1, 4) and (-2, -1).
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    238.

     Find a relation between x and y such that the points P(x, y) is equidistant from A(5, 1) and B(-1, 5).

     
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    239.

    Find a relation between x and y such that A(x, y) is equidistant from the points (a + b, b - a) and (a - b, a + b).

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    240.

    Find a relation between x and y such that P(x, y) is equidistant from the points A(-2, 5) and B( 1, -3).

    79 Views
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