State whether the two lines in each of the following are parallel, perpendicular or neither:
(i) Through (5, 6) and (2, 3); through (9, -2) and (6, -5)
(ii) Through (9, 5) and (-1, 1); through (3, -5) and (8, -3)
(iii) Through (6, 3) and (1, 1); through (-2, 5) and (2, -5)
(iv) Through (3, 15) and (16, 6); through (-5, 3) and (8, 2).
State whether the two lines in each of the following are parallel, perpendicular or neither:
(i) Through (5, 6) and (2, 3); through (9, -2) and (6, -5)
(ii) Through (9, 5) and (-1, 1); through (3, -5) and (8, -3)
(iii) Through (6, 3) and (1, 1); through (-2, 5) and (2, -5)
(iv) Through (3, 15) and (16, 6); through (-5, 3) and (8, 2).
(i) Slope of line joining (5, 6) and (2, 3)m1=y2−y1x2−x1=3−62−5=−3−3=1Slope of line joining (9, -2) and (6, -5)m2=y2−y1x2−x1=−5−(−2)6−9=−5+2−3=1Here m1=m2∴ The two lines are parallel.(ii) Slope of line joining (-1, 1) and (9, 5)m1=5−19−(−1)=410=25Slope of line joining (3, -5) and (8, -3)m2=−3−(−5)8−3=−3+55=25Here m1=m2∴ The two lines are parralel.(iii) Slope of line joining (6, 3) and (1, 1)m1=1−31−6=−2−5=25Slope of line joining (-2, 5) and (2, -5)m2=−5−52−(−2)=−104=−52Here m1×m2=25×−52=−1∴ The lines are perpendicular to each other.(iv) Slope of the line joining (3, 15) and (16, 6)m1=6−1516−3=−913Slope of line joining (-5, 3) and (8, 2)m2=2−38−(−5)=−113Here, neither m1−m2 nor m1×m2=−1∴ The lines are neither parallel nor perpendicular.
(i) Slope of line joining (5, 6) and (2, 3)m1=y2−y1x2−x1=3−62−5=−3−3=1Slope of line joining (9, -2) and (6, -5)m2=y2−y1x2−x1=−5−(−2)6−9=−5+2−3=1Here m1=m2∴ The two lines are parallel.(ii) Slope of line joining (-1, 1) and (9, 5)m1=5−19−(−1)=410=25Slope of line joining (3, -5) and (8, -3)m2=−3−(−5)8−3=−3+55=25Here m1=m2∴ The two lines are parralel.(iii) Slope of line joining (6, 3) and (1, 1)m1=1−31−6=−2−5=25Slope of line joining (-2, 5) and (2, -5)m2=−5−52−(−2)=−104=−52Here m1×m2=25×−52=−1∴ The lines are perpendicular to each other.(iv) Slope of the line joining (3, 15) and (16, 6)m1=6−1516−3=−913Slope of line joining (-5, 3) and (8, 2)m2=2−38−(−5)=−113Here, neither m1−m2 nor m1×m2=−1∴ The lines are neither parallel nor perpendicular.
