SOLUTION: Which of the lines 2x-y+3=0 and x-4y-7=0 is farther from origin?

Question 1043689: Which of the lines 2x-y+3=0 and x-4y-7=0 is farther from origin?
Found 2 solutions by Fombitz, ikleyn:
Answer by Fombitz(32388)   (Show Source): You can put this solution on YOUR website!
Find the slope of each line.

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The perpendicular line from the origin to each line has a slope that is the negative reciprocal of the given slope.

So then each line goes through the origin so the equation of each line is,

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Find the intersection point of each line,

So then,

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and

Then,

(,)
So then calculate the distance from the origin to the respective intersection points,

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Here's a graphical representation of the problem.
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Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
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Which of the lines 2x-y+3=0 and x-4y-7=0 is farther from origin?
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To answer your question, you have to calculate the distance from the point (0,0) (the origin of a coordinate system) to the given lines.

Read the lesson
    - The distance from a point to a straight line in a coordinate plane
in this site on how to do it.

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