Co Ordinate Geometry - Quantitative Aptitude Problems and Solutions

Area of a triangle :
          If A(x1,y1), B(x2,y2 and C(x3, y3) be three vertices of a ΔABC, then its area is given by:

		                            Δ = 1/2 [x1(y2 - y3 + x2(y3 - y1) + x3(y1 - y2)] 

  • 16.   Find the area of ΔABC whose vertices are A(9, -5), B(3, 7) and (-2, 4).

    A.) 29 units B.) 35.9 sq.units
    C.) 39 sq.units D.) 39.5 sq.units
    Answer: Option 'C'

    Here, x1 = 9, x2 = 3, x3 = -2 and y1 = -5, y2 = 7, y3 = 4

    = 1/2 [9(7-4) + 3(4+5) + (-2)(-5-7)]

    = 1/2 [9(3) + 3(9) - 2(-12)]

    = 1/2 [27 + 27 + 24]

    = 1/2 [78]

    = 39 sq.units



  • 17.   Find the area of ΔABC whose vertices are A(2, -5), B(4, 9) and (6, -1).

    A.) 9 units B.) 5 sq.units
    C.) 7 sq.units D.) 6 sq.units
    Answer: Option 'D'

    Here, x1 = 2, x2 = 4, x3 = 6 and y1 = -5, y2 = 9, y3 = -1

    = 1/2 [2(9+1) + 4(-1+5) + 6(5-9)]

    = 1/2 [2(10) + 4(4) + 6(-4)]

    = 1/2 [20 + 16 - 24]

    = 1/2 [12]

    = 6 sq.units



  • 18.  The points A(0, 6), B(-5, 3) and C(3, 1) are the vertices of a triangle which is ?

    A.) equilateral B.) right angled
    C.) isosceles D.) scalene
    Answer: Option 'C'

    AB2= (-5 - 0)2 + (-3 - 0)2 = 16 + 9 = 25

    BC2 = (3 + 5)2 + (1-3)2 = 82 + (-2)2 = 64 + 4 = 68

    AC2 = (3 - 0)2 + (1 - 6)2 = 9 + 25 = 34.

    AB = AC. ==> ΔABC is isosceles.



  • 19.   The points A(-4, 0), B(1, -4), and C(5, 1) are the vertices of

    A.) An isosceles right angled triangle B.) An equilateraltriangle
    C.) A scalene triangle D.) None of these
    Answer: Option 'A'

    AB2 = (1 + 4)2 + (-4 - 0)2

    = 25 + 16 = 41,

    BC2 = (5 - 1)2 + (1 + 4)2 = 42 + 52

    = 16 + 25 = 41

    AC2 = (5 + 4)2 + (1 - 0)2

    = 81 + 1 = 82

    AB = BC and AB2 = BC2 = AC2

    ΔABC is an isosceles right angled triangle



  • 20.   Find the vertices of triangle are A(2, 8), B(-4, 3) and (5, -1). The area of ΔABC is:

    A.) 5 1/2 sq.units B.) 2 1/3 sq.units
    C.) 2 1/2 sq.units D.) None of these
    Answer: Option 'C'

    Here, x1 = 2, x2 = -4, x3 = 5 and y1 = 8, y2 = 2, y3 = -1

    = 1/2 [2(3+1) - 4(-1-8) + 5(8-3)]

    = 1/2 [2(4) + 4(-9) + 5(5)]

    = 1/2 [16 - 36 + 25]

    = 1/2 [5]

    = 2 1/2 sq.units





  • Quantitative Aptitude Topics



    Quantitative Aptitude Topics


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