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Without using distance formula, show that the points (-2, 1), (5, 3), (6, 7) and (- 4, 5) are not the vertices of a parallelogram.

Asked by Topperlearning User 28th September 2017, 8:58 AM
Answered by Expert
Answer:

begin mathsize 12px style Let space the space given space points space be space straight A left parenthesis negative 2 comma space 1 right parenthesis comma space straight B left parenthesis 5 comma space 3 right parenthesis comma space straight C left parenthesis 6 comma space 7 right parenthesis space and space straight D left parenthesis negative 4 comma space 5 right parenthesis.
Slope space of space AB equals fraction numerator 3 minus 1 over denominator 5 plus 2 end fraction equals 2 over 7
Slope space of space CD equals fraction numerator 5 minus 7 over denominator negative 4 minus 6 end fraction equals fraction numerator negative 2 over denominator negative 10 end fraction equals 1 fifth
because space Slope space of space AB not equal to Slope space of space CD comma space AB space is space not space parallel space to space CD.
Therefore comma space square ABCD space is space not space straight a space parallelogram.
Hence comma space the space given space points space are space not space the space vertices space of space straight a space parallelogram. end style

Answered by Expert 28th September 2017, 10:58 AM
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