MathematicsThe points (−4,0), 4,0 , 0,3   are the vertices of a ____.

The points (4,0), 4,0 , 0,3   are the vertices of a ____.


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    Solution:

    The points (-4,0), (4,0), (0,3) are the vertices of an isosceles triangle.
    Given that, the points are (4,0), 4,0 , 0,3  .
    Let the points be A(-4, 0), B(4, 0) and C(0, 3).
    The distance formula between two points ( x 1 , y 1 ),( x 2 , y 2 )   is given by,
    x 2 x 1 2 + y 2 y 1 2  .
    Find the distance between the points AB:
    Here,
    ( x 1 , y 1 )=(4,0) ( x 2 , y 2 )=(4,0)  
    AB= (4(4)) 2 + (00) 2    =8   Distance between the points BC:
    Here,
    ( x 1 , y 1 )=(4,0) ( x 2 , y 2 )=(0,3)  
    BC= (04) 2 + (30) 2 = 16+9 =5    Distance between the points CA:
    Here,
    ( x 1 , y 1 )=(0,3) ( x 2 , y 2 )=(4,0)  
    CA= (40) 2 + (03) 2   =5  
    We know that if 2   points are equal in the vertices, then it is a vertex of an isosceles triangle.
    Here, BC=CA  .
    Hence, it is an isosceles triangle.
     
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