SOLUTION: The distance between the parallel lines y-x=2 and y=x+5 is ....... a)7/✓2 b)3/✓2. c)3/7. d)✓2/3

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Question 1083335: The distance between the parallel lines y-x=2 and y=x+5 is .......
a)7/✓2 b)3/✓2. c)3/7. d)✓2/3
Found 2 solutions by josgarithmetic, math_helper:
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
Line perpendicular to y=x+5 and having same y-intercept is y=-x+5.

Intersection point of y=x+2 with y=-x+5 occurs at ( 3/2, 7/2 ).

Distance between the two given lines of y=x+5 and y=x+2 is
sqrt%28%283%2F2-0%29%5E2%2B%287%2F2-5%29%5E2%29.
Simplify the value.

Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
(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