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 `(4 ,1 )`, where is the other end?

Answer 1

Coordinates of other endpoint (-107/10, -29/10)

Explanation:

Assumption : Its a perpendicular bisector.
Slope of line = `m_1`
`6y = 2x + 1`, Eqn (1)
`y = (1/3)x + (1/6)`
`m_1 = 1/3`
Slope of line segment (perpendicular) `m_2 = -1/m_1 = -3`

Equation of line segment is
`y - 1 = -3(x - 4)`
`3x + y = -11`, Eqn (2)

Solving Eqns (1) & (2),
Midpoint coordinates `x = -67/20, y = -19/20`

Other end point coordinates`(x_1, y_1)`
`(x_1+4)/2 = -67/20`
`x_1 = -107/10`

`(y_1 +1)/2 = -19/20`
`y-1 = -29/10`