A line segment is bisected by a line with the equation # 2 y - 2 x = 2 #. If one end of the line segment is at #( 3 , 8 )#, where is the other end?

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Answer 1 · 2017-07-22T08:53:55

The other end of the segment is #=(7,4)#

The equation of the line is

#y-x=1#

#y=x+1#.......................#(1)#

The slope of the line is #m=1#

The slope of the segment is #m'#

#mm'=-1#

#m'=-1#

The equation of the segment is

#y-8=-(x-3)#

#y=-x+3+8#

#y=-x+11#.......................#(2)#

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

#x+1=-x+11#

#2x=10#

#x=5#

#y=5+1=6#

The point of intersection is #=(5,6)#

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

Therefore,

#(5,6)=((a+3)/2,(b+8)/2)#

#(a+3)/2=5#

#a=10-3=7#

#(b+8)/2=6#

#b=12-8=4#