MathematicsState True/ False:The graph represents the arrangement of desks in a classroom. Ashima, Bharti and Camella are seated at A(3,1),B(6,4)   and C(8,6)   respectively. And A, B and C points are in line.

State True/ False:


The graph represents the arrangement of desks in a classroom. Ashima, Bharti and Camella are seated at A(3,1),B(6,4)   and C(8,6)   respectively. And A, B and C points are in line.


  1. A
    True
  2. B
    False  

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    Solution:

    Consider the given question,
    Here,
    We know that,
    If AB + BC = AC, then the points are collinear.
    So, let’s calculate AB, BC and AC.
    Using the distance formula;
    AB = x2-x12+y2-y12
    = 6-32+4-12
    = 32+32
    = 232
    = 23
    = 32
    Thus, AB is 32.
    Similarly, calculating BC,
    BC = x2-x12 +y2-y12  
    = (8-6)2+6-42
    = (2)2+22
    Solving further,
    = 22
    Thus, BC is 22.
    Calculating AC;
    AC = x2-x12 +y2-y12  
    = (8-(3)2+6-12
    = (5)2+52
    = 252
    = 52
    Now, finding if AB + BC = AC            ……(1)
    = 32 + 22  = 52
    Thus, AB + BC = AC
    Therefore, the points A, B and C are collinear.
    Hence, option 1 is true.
     
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