Question

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

Answer 1

Coordinates of other endpoint (-13/5, -61/5)

Explanation:

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

Equation of line segment is
`y - 7 = 2(x - 8)`
`2x - y = 9`, Eqn (2)

Solving Eqns (1) & (2),
Midpoint coordinates `x = 16/5, y = -13/5`

Other end point coordinates`(x_1, y_1)`
`(x_1+8)/2 = 16/5`
#x_1 = -(8/5)

`(y_1 +7)/2 = -13/5`
`y-1 = -(26/5) - 7 = -61/5`