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

Question

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

Aurora Ayala · Accepted Answer

#(4 1/2, -2 1/2)# #6y-2x=1# #6y=2x+1# #y=1/3x+1/6# The slope for this equation is #1/3#, therefor the slope for line segment,#m =-3# where #m*m_1=-1# The equation of line segment is #(y-y_1)=m(x-x_1)# where #x_1=2, y_1=5# #(y-5)=-3(x-2)# #y=-3x+6+5=-3x+11# #->a# so, the intercept between 2 lines is #1/3x+1/6=-3x+11# #2/6x+1/6=-3x+11# #2x+1=6(-3x+11)# #2x=-18x+66-1# #20x=65# #x = 65/20 = 13/4 =3 1/4# therefore, #y=-3(13/4)+11# #y=-39/4+44/4# #y=5/4=1 1/4# The line which intercept with both lines is a midpoint of the line segment. Therefore the other end line #(x,y)# #(x+2)/2=13/4#, #(y+5)/2=5/4# #x+2=13/2#, #y+5=5/2# #x=13/2-2#, #y=5/2-5# #x=9/2=4 1/2#, #y=-5/2=-2 1/2#

Sophia Alfred · Answer

undefined The other end of the line segment bisected by the line with the equation $6y - 2x = 1$ can be found by determining the intersection point of this line with the line segment. Given that one end of the line segment is at $(2, 5)$, we can use this information to find the coordinates of the other end.