SOLUTION: I need help finding the distance for this problem. Find the distance between parallel lines whose equations are y = -x + 2 and y = -x + 8. The answer choices are: A) 3 &#8

Question 928287: I need help finding the distance for this problem.
Find the distance between parallel lines whose equations are y = -x + 2 and y = -x + 8.
The answer choices are:
A) 3 √ 2
B) 2 √ 17
C) 10
D) 2 √ 29
(the √ is a square root bracket)
Thanks for your help in advance!
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Find the distance between parallel lines whose equations are
y = -x + 2 and y = -x + 8.
------
Draw the given lines.
One point on the 1st line is (0,2)
---
Find equation of the line perpendicular to the 1st line and
passing thur (0,2)::
y = mx + b
Solve for "b"
2 = 1*0 + b
b = 2
Equation: y = x + 2
-------
Find intersecetion of that line with the 2nd given line::
x+2 = -x+8
2x = 6
x = 3
y = -x+8
y = -3+8
y = 5
Intersection point is (3,5)
-----
Find distance of (0,2) to (3,5)
---
d = sqrt((5-2)^2+(3-0)^2) = sqrt(9 + 9) = 3sqrt(2)
==================================================
Cheers,
Stan H.
===================
The answer choices are:
A) 3 √ 2
B) 2 √ 17
C) 10
D) 2 √ 29

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