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CBSE Class 11-science Answered

Without using the Pythagoras theorem, prove that the points (– 2, 2), (8, – 2) and (– 4, – 3) are the vertices of a right angled triangle.
Asked by Topperlearning User | 20 Oct, 2016, 03:05: AM
answered-by-expert Expert Answer

Let these points A (-2, 2), B (8, -2) and C (-4, -3).

 
S l o p e space o f space A B space equals space fraction numerator minus 2 minus 2 over denominator 8 plus 2 end fraction equals minus 2 over 5 S l o p e space o f space B C equals fraction numerator minus 3 plus 2 over denominator minus 4 minus 8 end fraction equals 1 over 12 S l o p e space o f space A C equals fraction numerator minus 3 minus 2 over denominator minus 4 plus 2 end fraction equals 5 over 2 rightwards double arrow S l o p e space o f space A B space cross times space S l o p e space o f space A C equals minus 2 over 5 cross times 5 over 2 equals minus 1
 
Therefore, A,B and C are the vertices of a right angled triangle.
Answered by | 20 Oct, 2016, 05:05: AM

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