+128407 Rewrite the equations as
y= (5/12)x + 45/12 → y = (5/12)x + 15/4 (1)
y = (5/12)x + 46/12 → y = (5/12)x + 23/6
A perpendicular line to both of these will have a slope of (-12/5)
And if we let this line pass through (0, 23/6) we have the following equation
y = (-12/5)x + 23/6
To find the x intersection of this line and (1) we have
(5/12)x + 15/4 = (-12/5)x + 23/6
(5/12 + 12/5)x = 23/6 - 15/4
(169/60)x = 1/12
x = (1/12) (60/169) = 5/169
And y = (5/12) (5/169) + 15/4 = 3815/1014
The distance between these lines =
sqrt [ (5/169)^2 + ( 23/6 - 3815/1014)^2 ] = 1/13 units
