Question

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?

Answer 1

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`