SOLUTION: Find a point (x,y) equidistant from lines 2x+5y-8=0 and 3x-4y+3=0

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Question 1128772: Find a point (x,y) equidistant from lines 2x+5y-8=0 and 3x-4y+3=0
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Find a point (x,y) equidistant from lines 2x+5y-8=0 and 3x-4y+3=0
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A line is equidistant, not just one point.
The most obvious point is the intersection.
(17/23,30/23)

Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.
The locus (the set) of the points equidistant from the two given intersecting lines is the bisector of the angle formed by the lines.



More exactly, the two given intersecting lines form 4 (four) angles in the plane, 

so the locus (the set) of the points equidistant from the two given intersecting lines are 4 (four) bisectors 

of the 4 (four) angles formed by the lines.



These bisectors, in turn, form two straight lines.