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begin mathsize 12px style If space straight P left parenthesis 2 comma space minus 5 right parenthesis comma space straight Q left parenthesis negative 2 comma space 5 right parenthesis comma space straight R left parenthesis straight x comma space 3 right parenthesis space and space straight S left parenthesis 1 comma space 1 right parenthesis space be space the space four space points space such space that space PQ perpendicular RS comma space
find space the space value space of space straight x. end style

Asked by Topperlearning User 28th September 2017, 8:38 AM
Answered by Expert
Answer:

begin mathsize 12px style straight P space left parenthesis 2 comma space minus 5 right parenthesis space comma space straight Q space left parenthesis space minus 2 comma space 5 right parenthesis
Slope space of space PQ equals straight m subscript 1 equals fraction numerator 5 plus 5 over denominator negative 2 minus 2 end fraction equals fraction numerator 10 over denominator negative 4 end fraction equals negative 5 over 2
straight R space left parenthesis straight x comma space 3 right parenthesis comma space straight S space left parenthesis 1 comma space 1 right parenthesis
Slope space of space RS equals straight m subscript 2 equals fraction numerator 1 minus 3 over denominator 1 minus straight x end fraction equals negative fraction numerator 2 over denominator 1 minus straight x end fraction
Since space PQ perpendicular RS comma space
straight m subscript 1 cross times straight m subscript 2 equals negative 1
therefore space minus 5 over 2 cross times open parentheses negative fraction numerator 2 over denominator 1 minus straight x end fraction close parentheses equals negative 1
therefore space fraction numerator 5 over denominator 1 minus straight x end fraction equals negative 1
therefore space 5 equals negative 1 plus straight x
therefore space straight x equals 6 end style

Answered by Expert 28th September 2017, 10:38 AM
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