Co Ordinate Geometry - Quantitative Aptitude Problems and Solutions

    Division of a line segment by a point :  
    a) If a points P(x,y) divides the join of A(x1, y1) and B(x2, y2) in the ratio m : n, then
    x = (mx2 + nx1)/m+n and y = (my2 + ny1)/m+n
    b) If A(x1, y1) and B(x2, y2) be the end points of a line segment AB, then the co-ordinates of
    mid-point of AB are
    (x1 + x2)/2, (y1 + y2)/2].


  1. 25.   Find the co-ordinates of the centroid of ΔABC whose vertices are A(7, -3), B(5, -4) and C(-3, -5)?

    A.) 3, -3 B.) 3, -4
    C.) 4, -3 D.) None of these
    Answer: Option 'B'

    x1 = 7, x2 = 5, x3 = -3 and y1 = -3, y2 = -4, y3 = -5

    = [(7 + 5 - 3)/3, (-3 - 4 - 5)/3]

    = (12-3)/3, -12/3)

    = (9/3, -12/3)

    = (3, -4)



  2. 26.   The co-ordinates of the end points of a diameter AB of a circle are A(-6, 8) and B(-10, 6). Find the

           co-ordinates of its centre.

    A.) -8, 7 B.) -7, 8
    C.) 7, -8 D.) -8, -7
    Answer: Option 'A'

    The center O is the mid point of AB.

    Co-ordinates of O are [(-6-10)/2, (8+6)/2]

    = -16/2, 14/2

    = (-8, 7)



  3. 27.  Find the co-ordinates of a point P which divides the join of A(5, -4) and B(10, 8) in the ratio 3 : 2.

    A.) 9, 5 B.) 7, 8
    C.) 8, 7 D.) 9, -7
    Answer: Option 'C'

    Required point is P = (mx2 + nx1)/m+n, (my2 + ny1)/m+n

    P((3(10) + 2(5))/5, (3(15) + 2(-5))/5)

    =(30 + 10)/5, (45-10)/5

    = P(8, 7)



  4. 28.  A point C divides the join of A(2,5) and B(3,9) in the ratio 3 : 4. The co-ordinates of C are:

    A.) (15/7, 46/7) B.) (15/7, 47/7)
    C.) (15/7, 40/7) D.) None of these
    Answer: Option 'B'

    x1=2, x2=3 and y1=3, y2=7

    = [(3*3 + 4*2)/7, (3*9 + 4*5)/7]

    = 9+6/7, 27+20/7

    = (15/7, 47/7)



  5. 29.   The end points of a line segment AB are A(-6, 4) and B(12,24). Its midpoint is:

    A.) (14, 4) B.) (-4, 14)
    C.) (3, 14) D.) (-3, 14)
    Answer: Option 'C'

    Midpoint is C((-6+12)/2, (4+24)/2)

    (-6/2, 28/2) = (-3, 14)




Quantitative Aptitude Topics


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