MathematicsThe kind of triangle formed from these points A(−5,6),B(−4,−2)   and C(7,5)   is ____.

The kind of triangle formed from these points A(5,6),B(4,2)   and C(7,5)   is ____.


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    Solution:

    Given that, the points A(5,6),B(4,2)   and C(7,5)  .
    The distance formula between two points ( x 1 , y 1 ),( x 2 , y 2 )   is given by,
    d= x 2 x 1 2 + y 2 y 1 2  
    Find the distance of AB  .
    d= x 2 x 1 2 + y 2 y 1 2 d= 4 5 2 + 26 2 d= 1 2 + 8 2   d= 1+64 d= 65  
    Find the distance of AC.
    d= x 2 x 1 2 + y 2 y 1 2 d= 7 5 2 + 56 2 d= 12 2 + 1 2   d= 144+1 d= 145  
    Find the distance of BC.
    d= x 2 x 1 2 + y 2 y 1 2 d= 7 4 2 + 5 2 2 d= 11 2 + 7 2   d= 121+49 d= 170  
    A scalene triangle is a triangle whose three sides all have different lengths.
    Here, AB ≠ BC ≠ AC.
    Hence ABC  is a scalene triangle.
    Hence, the required answer is scalene triangle.
     
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