How do you find the perpendicular distance between the straight lines #y=2x+7# and #y=2x+2#?

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Answer 1 · 2015-11-30T15:31:35

#5/ sqrt 5 = sqrt 5#

#r : y = 2x + 7#

#s : y = 2x + 2#

#r# and #s# are parallel, and both are perpendicular to

#t : y = -1/2 x + b#

Let #b = 0# and find #r cap t = P, s cap t = Q#

#2x + n = -1/2 x#

#4x + 2n = -x#

#x = - (2n) / 5#

#y = -1/2 x = n/5#

#|PQ|^2 = (-(2n_1)/5 + (2n_2)/5)^2 + ((n_1)/5 - (n_2)/5)^2#

#|PQ|^2 = 4/25 (n_2 - n_1)^2 + 1/25 (n_1 - n_2)^2#

#|PQ| = sqrt {1/5} |n_1 - n_2|#

#n_1 = 7, n_2 = 2#