Question

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

Answer 1

Coordinates of other end = (67/29, 8/29) or (2.3103, 0.2759)

Explanation:

Assumption : Given line equation is a perpendicular bisector to the line segment

`3x - 7y = 2 color (white)(aaa)` Eqn (1)
`y = (3/7)x - (2/7)`
Slope of line m1 = 3/7.
Slope of perpendicular line segment `= -1 / (m1 )= -1 / (3/7) = -7/3`

`y - 1 = -(7/3) (x - 2)`
#7x + 3y = 17 color(white)(aaa) Eqn (2)

Solving Eqns (1) & (2),
`x = 125/58, y = 37/58`

`(2+x_1) / 2 = 125/58`
`x_1 = (125 - 58)/ 29 =67/29`
`(1+y_1) / 2 = 37/58`
`y_1 = 8/29`