A line segment is bisected by a line with the equation # 4 y - 3 x = 2 #. If one end of the line segment is at #( 2 , 1 )#, where is the other end?

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Answer 1 · 2017-01-24T17:20:56

#(1 1/25,2 7/25)#

#4y-3x=2#, #4y=3x+2#
#y=3/4x+1/2# #->a#

gradient of the other line, #m = -1/(3/4)=-4/3#

The equation of the line thru #(2,1)#,

#y-y_1=m(x-x_1)#
#y-1=-4/3(x-2)#
#y=-4/3x+8/3+1#
#y=-4/3x+11/3#

replacing y from #a#

#3/4x+1/2=-4/3x+11/3#

#3/4x+4/3x=11/3-1/2#

#9/12x+16/12x=22/6-3/6#

#25/12x=19/6#

#x=19/6*12/25=38/25#

#y=3/4(38/25)+1/2#

#y=57/50+25/50=82/50=41/25#

#(38/25,41/25)# is a midpoint of the line.

The other end of the line, #(x,y)#.

#(x+2)/2=38/25#
#x=38/25*2-2#
#x=76/25-50/25=26/25=1 1/25#

#(y+1)/2=41/25#
#y=41/25*2-1#
#y=82/25-25/25=57/25=2 7/25#

The other end #(1 1/25,2 7/25)#