determine the points L ( -1 , 1) , M (8,5) , N ( 5,6) are vertices of a right triangle or not
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For right triangle, LN² = LM² + MN² [ Pythagoras Theorem]
LN² = [ √( 5+ 1 )² + ( 6 - 1 )²] ²
LN² = 36 + 25 = 61
LM² = [ √( 8 +1 )² + ( 5 - 1 ) ² ] ²
LM² = 81 + 16 = 97
MN² = [√( 5 - 8 )² + ( 6 - 5 ) ²] ²
MN² = 9 + 1 = 10
LN² = LM² + MN²
R. H. S. = 97 + 10 = 107
L. H. S.= 61
L. H. S. ≠ R. H. S.
=> The given points are not the vertices of a triangle.
LN² = [ √( 5+ 1 )² + ( 6 - 1 )²] ²
LN² = 36 + 25 = 61
LM² = [ √( 8 +1 )² + ( 5 - 1 ) ² ] ²
LM² = 81 + 16 = 97
MN² = [√( 5 - 8 )² + ( 6 - 5 ) ²] ²
MN² = 9 + 1 = 10
LN² = LM² + MN²
R. H. S. = 97 + 10 = 107
L. H. S.= 61
L. H. S. ≠ R. H. S.
=> The given points are not the vertices of a triangle.
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