Question

A line segment is bisected by a line with the equation `4 y + 3 x = 4`. If one end of the line segment is at `( 8 , 1 )`, where is the other end?

Answer 1

`P=(56/25;-167/25)`

Explanation:

Calculate the normal passing per `A=(8;1)`
`m=-3/4`
`m_(|--)=4/3`
Normal equation
`y-1=4/3(x-8)`
`4x-3y=29`
Calculate intersection I
`{(3x+4y=4),(4x-3y=29):}`
Solving the system you get `I=(128/25;-71/25)`
Calculate `P` so that `I` is the medium point of `bar(PA)`
`{((P_x+8)/2=128/25),((p_y+1)/2=-71/25):}`
`P_x=56/25`
`P_y=-167/25`