SOLUTION: How do you find the distance between x+3y=6 and x+3y=-14 if they are both parallel lines?
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Question 510101: How do you find the distance between x+3y=6 and x+3y=-14 if they are both parallel lines?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Pick a point on either line. Write an equation of a line that passes through the point you selected and is perpendicular to the line containing that point. Remember, the slopes of perpendicular lines are negative reciprocals of each other. Use the point-slope form:
 )
where )
are the coordinates of the given point and 
is the given/calculated slope.
Once you have the equation of the perpendicular to the line you chose at the start, solve the system of equations formed by the OTHER given line and the perpendicular.
The solution set of the above described system is the point of intersection between the perpendicular and the line NOT chosen in the first step. Find the distance from the point you selected in the first step and the point of intersection that you just calculated. Use the distance formula:
^2\ +\ (y_1\ -\ y_2)^2})
where and )
are the coordinates of the two points of intersection.
John
My calculator said it, I believe it, that settles it
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