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Show that the line joining the points A(2, -3) and B(-5, 1) is parallel to the line joining the points C(7, -1) and D(0, 3) and perpendicular to the line joining the points P(4, 5) and Q(0, -2).

Asked by Topperlearning User 28th September 2017, 8:34 AM
Answered by Expert
Answer:

begin mathsize 12px style straight A left parenthesis 2 comma space minus 3 right parenthesis space and space straight B left parenthesis negative 5 comma space 1 right parenthesis
Slope space of space line space AB equals fraction numerator 1 minus left parenthesis negative 3 right parenthesis over denominator negative 5 minus 2 end fraction equals negative 4 over 7
straight C left parenthesis 7 comma space minus 1 right parenthesis space and space straight D left parenthesis 0 comma space 3 right parenthesis
Slope space of space line space CD equals fraction numerator 3 space minus space open parentheses negative 1 close parentheses over denominator 0 minus 7 end fraction equals negative 4 over 7
Since comma space slope space of space line space AB equals slope space of space line space CD comma space AB space parallel to space CD.
straight P left parenthesis 4 comma space 5 right parenthesis space and space straight Q left parenthesis 0 comma space minus 2 right parenthesis.
Slope space of space line space PQ equals fraction numerator negative 2 minus 5 over denominator 0 minus 4 end fraction equals 7 over 4
Now comma space Slope space of space line space AB cross times slope space of space line space PQ equals negative 4 over 7 cross times 7 over 4 equals negative 1.
Hence comma space AB perpendicular PQ. end style

Answered by Expert 28th September 2017, 10:34 AM
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