6y-2x=16y−2x=1
6y=2x+16y=2x+1
y=1/3x+1/6y=13x+16
The slope for this equation is 1/313, therefor the slope for line segment,m =-3m=−3 where m*m_1=-1m⋅m1=−1
The equation of line segment is (y-y_1)=m(x-x_1)(y−y1)=m(x−x1) where x_1=2, y_1=5x1=2,y1=5
(y-5)=-3(x-2)(y−5)=−3(x−2)
y=-3x+6+5=-3x+11y=−3x+6+5=−3x+11 ->a→a
so, the intercept between 2 lines is
1/3x+1/6=-3x+1113x+16=−3x+11
2/6x+1/6=-3x+1126x+16=−3x+11
2x+1=6(-3x+11)2x+1=6(−3x+11)
2x=-18x+66-12x=−18x+66−1
20x=6520x=65
x = 65/20 = 13/4 =3 1/4x=6520=134=314
therefore,
y=-3(13/4)+11y=−3(134)+11
y=-39/4+44/4y=−394+444
y=5/4=1 1/4y=54=114
The line which intercept with both lines is a midpoint of the line segment. Therefore the other end line (x,y)(x,y)
(x+2)/2=13/4x+22=134, (y+5)/2=5/4y+52=54
x+2=13/2x+2=132, y+5=5/2y+5=52
x=13/2-2x=132−2, y=5/2-5y=52−5
x=9/2=4 1/2x=92=412, y=-5/2=-2 1/2y=−52=−212