A line segment is bisected by a line with the equation # - 5 y + 2 x = 1 #. If one end of the line segment is at #(6 ,4 )#, where is the other end?

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Answer 1 · 2017-07-14T08:24:25

The coordinates of the other end is #=(210/29,28/29)#

The equation of the line is

#-5y+2x=1#

#5y=2x-1#

#y=2/5x-1/5#.......................#(1)#

The slope of the line is #m=2/5#

The slope of the segment is #m'#

#mm'=-1#

#m'=-5/2#

The equation of the segment is

#y-4=-5/2(x-6)#

#y=-5/2x+15+4#

#y=-5/2x+19#.......................#(2)#

Solving for #x# and #y# in the equations #(1)# and #(2)# gives the point of intersection of the line and the segment

#-5/2x+19=2/5x-1/5#

#2/5x+5/2x=19+1/5#

#29/10x=96/5#

#x=96/5*10/29=192/29#

#y=2/5*192/29-1/5=71/29#

Let the other end of the segment be #=(a,b)#

Therefore,

#(192/29,71/29)=((a+6)/2,(b+4)/2)#

#(a+6)/2=192/29#

#a=384/29-6=210/29#

#(b+4)/2=71/29#

#b=144/29-4=28/29#