Question 1083335
(1)  y = x + 2     (intercepts y-axis at (0,2))
(2) y = x + 5     (intercepts y-axis at (0,5))

A line perpendicular to both of these will have slope  -(1/m) = -1/1 = -1,
and equation  y = -x + b.   Pick point on (1) or (2) to plug in to find 'b'.
I chose (0,5):   5 = -(0) + b ==>  b=5, so the perpendicular has eqn y=-x+5.

This intersects line (1) where the perpendicular and line (1) have the same y
value:
             y = -x+5 = x+2   ==>  2x = 3 ==> x = 3/2 —> y=7/2

Distance is then  {{{ sqrt((3/2-0)^2 + (7/2-5)^2) = sqrt(9/4 + 9/4) = sqrt(18/4) = (3/2)sqrt(2) = 3/sqrt(2) }}}