If point p(2,1) is on the line segment a(4,2) and b(8,4);then prove the relation that ap=1/2ab.

Asked by priyanka2883pandey | 29th May, 2020, 10:35: PM

Expert Answer:

p(2,1) is on the line segment joining the points a(4,2) and b(8,4)
Using Distance formula,
a p equals square root of open parentheses 4 minus 2 close parentheses squared plus open parentheses 2 minus 1 close parentheses squared end root equals square root of 2 squared plus 1 end root equals square root of 5
a b equals square root of open parentheses 4 minus 8 close parentheses squared plus open parentheses 2 minus 4 close parentheses squared end root equals square root of 4 squared plus 2 squared end root equals square root of 20 equals 2 square root of 5
a p equals square root of 5 equals fraction numerator 2 square root of 5 over denominator 2 end fraction equals 1 half a b
H e n c e comma space a p equals 1 half a b

Answered by Renu Varma | 31st May, 2020, 01:07: PM

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