Question

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?

Answer 1

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

Explanation:

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`