A line segment is bisected by a line with the equation - 6 y + 2 x = 4 . If one end of the line segment is at ( 4 , 8 ), where is the other end?

1 Answer
Nov 3, 2016

The other point is B(42/5;-26/5)

Explanation:

the given line has slope m=1/3 so the segment must have slope m'=-3 and the line where lies the segment AB has equation y=-3(x-4)+8.

If we find the instersection between these two lines, this represents the medium point between A and B

By replacing the second equation into the first we obtain
2x-6(-3(x-4)+8)-4=0 that solved for x gives the coordinates of
M(31/5;7/5)

At this point if B(t, u), it must be (t+4)/2=31/5 and (u+8)/2=7/5 that solved yeld t=42/5 and u=-26/5