Question

A line segment is bisected by a line with the equation `3 y - 7 x = 2`. If one end of the line segment is at `( 8 , 1 )`, where is the other end?

Answer 1

Coordinates of other end points (-6.6,3.6)

Explanation:

Assumption : Bisecting line is a perpendicular bisector

Standard form of equation `y=max+c`
Slope of perpendicular bisector m is given by
`3y-7x=2`
`y=(7/3)x+(2/3)`
`m=7/3`
Slope of line segment is
`y-1=-(1/m)(x-8)`
`y-1=-(3/7)(x-8)`
`7y-7=3x-24`

`7y-3x=-14color(white)((aaaa)` Eqn (1)
`3y-7x=2color(white)((aaaa)` Eqn (2)

Solving Eqns (1) & (2),
`21y-9x=42`
`21y-49x=14`
Subtracting and eliminating y term,
`40x=28`
`x=7/10`
Substituting value of x in Eqn (1),
`7y-(21/10)=14`
`y=(161/10)/7=23/10`
Mid point #(7/10,23/10)

Let (x1,y1) the other end point.
`(8+x1)/2=7/10`
`x1=-6.6`
`(1+y1)/2=23/10`
`y1=3.6`

Coordinates of other endpoint `(-6.6,3.6)`