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Without using the Pythagoras theorem, show that the points (5, 5), (4, 6) and (2, 2) are the vertices of a right-angled triangle.

Asked by Topperlearning User 28th September 2017, 8:48 AM
Answered by Expert

begin mathsize 12px style Let space the space three space points space be space straight P left parenthesis 5 comma space 5 right parenthesis comma space straight Q left parenthesis 4 comma space 6 right parenthesis space and space straight R left parenthesis 2 comma space 2 right parenthesis.
Slope space of space PQ equals fraction numerator 6 minus 5 over denominator 4 minus 5 end fraction equals negative 1 over 1 equals negative 1
Slope space of space PR equals fraction numerator 2 minus 5 over denominator 2 minus 5 end fraction equals fraction numerator negative 3 over denominator negative 3 end fraction equals 1
Now comma space product space of space the space slopes space of space PQ space and space PR equals 1 cross times left parenthesis negative 1 right parenthesis equals negative 1
rightwards double arrow space PQ perpendicular PR
Therefore comma space increment PQR space is space straight a space right minus angled space triangle.
Hence comma space the space given space points space are space the space vertices space of space straight a space right minus angled space triangle. end style

Answered by Expert 28th September 2017, 10:48 AM
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