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Question

Prove that the line $$5x-2y-1=0$$ is mid-parallel to the lines $$5x-2y-9=0$$ and $$5x-2y+7=0$$.


Solution

Let lines be $${ l }_{ 1 }=5x-2y-1=0$$
                    $${ l }_{ 2 }=5x-2y-9=0$$
                    $${ l }_{ 3 }=5x-2y+7=0$$
Slope of $${ l }_{ 1 }=5/2$$
Slope of $${ l }_{ 2 }=5/2$$
Slope of $${ l }_{ 3 }=5/2$$
dist. b/w $${ l }_{ 1 }\& { l }_{ 2 }=\dfrac { 1-9+11 }{ \sqrt { 25+4 }  } =\dfrac { 8 }{ \sqrt { 29 }  } $$
dist b/w $${ l }_{ 1 }\& { l }_{ 3 }=\dfrac { 1-1-71 }{ \sqrt { 25+4 }  } =\dfrac { 8 }{ \sqrt { 29 }  } $$
Hence $${ l }_{ 1 }$$ is mid parallel to $${ l }_{ 2 }\& { l }_{ 3 }$$.

Mathematics

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