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).

CBSE Class 11-science Answered

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 | 28 Sep, 2017, 08:34: AM

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 | 28 Sep, 2017, 10:34: AM