Determine which of the lines L 1 , L 2 L _ { 1 } , L _ { 2 } L 1 , L 2 and L 3 L _ { 3 } L 3 passing through the indicated pairs of points are parallel. L 1 ( − 2 , − 7 ) , ( 0 , 1 ) L 2 ( − 2 , 11 ) , ( 5 , − 24 ) L 3 ( 0 , − 2 ) , ( 5 , 18 ) \begin{array} { |l|l|} \hline L _ { 1 } & ( - 2 , - 7 ) , ( 0,1 ) \\hline{ L _ { 2 } } & (-2,11) ,(5,-24) \\hline{ L _ { 3 } } & (0,-2) ,(5,18) \\hline\end{array} L 1 L 2 L 3 ( − 2 , − 7 ) , ( 0 , 1 ) ( − 2 , 11 ) , ( 5 , − 24 ) ( 0 , − 2 ) , ( 5 , 18 ) A) L 1 and L 3 L _ { 1 } ext { and } L _ { 3 } L 1 and L 3 B) L 1 and L 2 L _ { 1 } ext { and } L _ { 2 } L 1 and L 2 C) L 2 and L 3 L _ { 2 } ext { and } L _ { 3 } L 2 and L 3 D) all are parallelE) none are parallel

Question

Determine which of the lines   L 1 , L 2 L _ { 1 } , L _ { 2 } L 1 ​ , L 2 ​   and   L 3 L _ { 3 } L 3 ​   passing through the indicated pairs of points are parallel. L 1 ( − 2 , − 7 )  , ( 0 , 1 )  L 2 ( − 2 , 11 )  , ( 5 , − 24 )  L 3 ( 0 , − 2 )  , ( 5 , 18 )  \begin{array} { |l|l|} \hline L _ { 1 }  &  ( - 2 , - 7 )  , ( 0,1 ) \\hline{ L _ { 2 } } & (-2,11) ,(5,-24)  \\hline{ L _ { 3 } }  & (0,-2) ,(5,18) \\hline\end{array} L 1 ​ L 2 ​ L 3 ​ ​ ( − 2 , − 7 )  , ( 0 , 1 )  ( − 2 , 11 )  , ( 5 , − 24 )  ( 0 , − 2 )  , ( 5 , 18 )  ​ ​ A)    L 1  and  L 3 L _ { 1 } 	ext { and } L _ { 3 } L 1 ​  and  L 3 ​ B)    L 1  and  L 2 L _ { 1 } 	ext { and } L _ { 2 } L 1 ​  and  L 2 ​ C)    L 2  and  L 3 L _ { 2 } 	ext { and } L _ { 3 } L 2 ​  and  L 3 ​ D) all are parallelE) none are parallel

Saroj Sharma · Accepted Answer

Final Answer : A, Explanation :   The slopes of the lines are calculated as follows:    L 1 L_1 L 1 ​  :   1 − ( − 7 ) 0 − ( − 2 ) = 8 2 = 4 \frac{1 - (-7)}{0 - (-2)} = \frac{8}{2} = 4 0 − ( − 2 ) 1 − ( − 7 ) ​ = 2 8 ​ = 4      L 2 L_2 L 2 ​  :   − 24 − 11 5 − ( − 2 ) = − 35 7 = − 5 \frac{-24 - 11}{5 - (-2)} = \frac{-35}{7} = -5 5 − ( − 2 ) − 24 − 11 ​ = 7 − 35 ​ = − 5      L 3 L_3 L 3 ​  :   18 − ( − 2 ) 5 − 0 = 20 5 = 4 \frac{18 - (-2)}{5 - 0} = \frac{20}{5} = 4 5 − 0 18 − ( − 2 ) ​ = 5 20 ​ = 4    Since   L 1 L_1 L 1 ​   and   L 3 L_3 L 3 ​   have the same slope, they are parallel.

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