SOLUTION: Hi can you please show me how to find the distance between the parallel lines :y=2x-4 and y=2x+1 Thank you Nicole

Question 112978This question is from textbook Geometry
: Hi can you please show me how to find the distance between the parallel lines
:y=2x-4 and y=2x+1
Thank you
Nicole
This question is from textbook Geometry

Answer by veronica0626(5) (Show Source): You can put this solution on YOUR website!

First we need to know that the distance between parallel line is the distance of EVERY segment perpendicular to the given lines.
we emphasize the word every because the distance is equal for every segment.
to find that segment we should name one line perpendicular to the two given lines.
(any line perpindicular would do)
since the slope of the parallel lines is 2, the slope of the line perpendicular to it is -2 (there's a theorem for that)
i name my perpendicular line y=-2x+1 represented by the blue line
(y=2x+4 is red and y=2x+1 is green)
then we find the intersection of y=2x+1 and y=-2x+1
by elimination or substitution
we get x=0 and y=1/2, then the intersection is (0,1/2)
and the intersection of y=2x-4 and y=-2x+1
by elimination or substition
we get x=3/4 and y 5/2, then the intersection is (3/4 , 5/2)
these points are the endpoints of the segment perpendicular to the given lines.
getting the distance, we follow the formula
AMP Parsing Error of [
First we need to know that the distance between parallel line is the distance of EVERY segment perpendicular to the given lines.
we emphasize the word every because the distance is equal for every segment.
to find that segment we should name one line perpendicular to the two given lines.
(any line perpindicular would do)
since the slope of the parallel lines is 2, the slope of the line perpendicular to it is -2 (there's a theorem for that)
i name my perpendicular line y=-2x+1 represented by the blue line
(y=2x+4 is red and y=2x+1 is green)
then we find the intersection of y=2x+1 and y=-2x+1
by elimination or substitution
we get x=0 and y=1/2, then the intersection is (0,1/2)
and the intersection of y=2x-4 and y=-2x+1
by elimination or substition
we get x=3/4 and y 5/2, then the intersection is (3/4 , 5/2)
these points are the endpoints of the segment perpendicular to the given lines.
getting the distance, we follow the formula
]: Invalid expression 'FirstweneedtoknowthatthedistancebetweenparallellineisthedistanceofEVERYsegmentperpendiculartothegivenlines.weemphasizethewordeverybecausethedistanceisequalforeverysegment.tofindthatsegmentweshouldnameonelineperpendiculartothetwogivenlines.(anylineperpindicularwoulddo)sincetheslopeoftheparallellinesis2,theslopeofthelineperpendiculartoitis-2(there'satheoremforthat)inamemyperpendicularliney=-2\x+1representedbytheblueline(y=2\x+4isredandy=2\x+1isgreen)thenwefindtheintersectionofy=2\x+1andy=-2\x+1byeliminationorsubstitutionwegetx=0andy=1/2,thentheintersectionis(0,1/2)andtheintersectionofy=2\x-4andy=-2\x+1byeliminationorsubstitionwegetx=3/4andy5/2,thentheintersectionis(3/4,5/2)thesepointsaretheendpointsofthesegmentperpendiculartothegivenlines.gettingthedistance,wefollowtheformula': syntax error at /home/ichudov/project_locations/algebra.com/templates/Algebra/Expression.pm line 203. .
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