Answer :

Given: parallel lines 12x – 5y – 3 = 0, 12x – 5y + 7 = 0, 12x – 5y – 13 = 0


To Prove : line 12x – 5y – 3 = 0 is mid-parallel to the lines 12x – 5y + 7 = 0 and 12x – 5y – 13 = 0


Formula used :


The distance between the parallel lines ax + by + c =0 and ax + by + d =0 is,


D


The equation of line l is 12x – 5y + 7 = 0


The equation of line m is 12x – 5y – 3 = 0


The equation of line n is 12x – 5y – 13 = 0



Let D1 be the distance between the lines l and m .


Here a = 12 ,b = -5 ,c = 7 ,d = -3


D1..


The distance between the parallel lines l and m is units


Let D2 be the distance between the lines m and n .


Here a = 12 ,b = -5 ,c = 7 ,d = -3


D2


The distance between the parallel lines m and n is units


Distance between the parallel lines l and m = Distance between the parallel lines m and n


Thus the line 12x – 5y – 3 = 0 is mid-parallel to the lines 12x – 5y + 7 = 0 and 12x – 5y – 13 = 0


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