Co Ordinate Geometry - Quantitative Aptitude Problems and Solutions

    Various types of quadrialterals:-

      A quadrilateral is 
    i) A rectangle if its opposite sides are equal and diagonals are equal.
    ii) A parallelogram but not a rectangle, if its opposite sides are equal and the diagonals are not equal.
    iii) A square, if all sides are equal and diagonals are equal.
    iv) Rhombus but not a square, if all sides are equal and diagonals are not equal


  1. 30.   The vertices of a ΔABC are A(-6, 18), B(12, 0) and C(9, −21). The centroid of ΔABC is:

    A.) (5, 1) B.) (5, -1)
    C.) (4, -1) D.) None of these
    Answer: Option 'B'

    CENTROID OF A TRIANGLE

    The point of intersection of all the medians of a triangle is called its centroid.

    If A(x1, y1), B(x2, y2) and C(x3, y3) be the vertices of ΔABC,

    then the co-ordinates of its centroid are [1/3(x1 + x2 + x3), 1/3(y1 + y1 + y3)]

    = [1/3(-6+12+9), 1/3(18+0-21)]

    = [15/3, -3/3]

    = (5, -1)



  2. 31.   The vertices of a quadrilateral ABCD are A(0, 0), B(3,3), C(3, 6) and D(0, 3). Then , ABCD is a

    A.) square B.) parallelogram
    C.) rectangle D.) rhombus
    Answer: Option 'B'

    AB2 = (3-0)2 + (3-0)2 = 18

    BC2 = (3-3)2 + (6-3)2 = 9

    CD2 = (0-3)2 + (3-6)2 =18

    AD2 = (0-0)2 + (3-0)2 = 9

    AB = CD = √18 => 3√2,

    BC = AD = √9

    AC2 = (3-0)2 + (6-0)2 = 9 + 36 = 45

    BD2 = (0-3)2 + (3-3)2 = 9 + 0 = 9

    AC ≠ BD

    ABCD is a parallelogram.



  3. 32.  The points A(1, -3), B(13, 9), C(10, 12) and D(-2, 0) taken in order are the vertices of

    A.) square B.) rhombus
    C.) parallelogram D.) rectangle
    Answer: Option 'D'

    AB2 = (13-1)2 + (9+3)2

    = 122 + 122 = 288.

    BC2 = (10-13)2 + (12-9)2

    = -32 + 32 = 9+9 = 18

    CD2 = (10+2)2 + (12-0)2

    = 122 + 122 = 288

    AD2 = (-2-1)2 + (0+3)2 = (9+9) =18

    AB = CD and BC = AD

    AC2 = (10-1)2 + (12+3)2

    = 92 + 152 = 81 + 225 = 306.

    BD2 = (-2-13)2 + (0-9)2

    = 225 + 81 = 306

    AC = BD

    ABCD is a rectangle.



  4. 33.   If for a line m = tanϑ < 0, then

    A.) ϑ is acute B.) ϑ is obtuse
    C.) ϑ = 90° D.) ϑ = 60°
    Answer: Option 'B'

    m = tanϑ < 0 => is obtuse



  5. 34.   If for a line m = tanϑ > 0, then

    A.) ϑ is acute B.) ϑ is obtuse
    C.) ϑ = 90° D.) ϑ = 60°
    Answer: Option 'A'

    m = tanϑ < 0 => is acute





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