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

1 Answer
Oct 28, 2016

P=(56/25;-167/25)P=(5625;16725)

Explanation:

Calculate the normal passing per A=(8;1)A=(8;1)
m=-3/4m=34
m_(|--)=4/3m=43
Normal equation
y-1=4/3(x-8)y1=43(x8)
4x-3y=294x3y=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