A line segment is bisected by line with the equation 6 y - 2 x = 1 6y2x=1. If one end of the line segment is at (2 ,5 )(2,5), where is the other end?

1 Answer
Jan 26, 2017

(4 1/2, -2 1/2)(412,212)

Explanation:

6y-2x=16y2x=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=-1mm1=1

The equation of line segment is (y-y_1)=m(x-x_1)(yy1)=m(xx1) where x_1=2, y_1=5x1=2,y1=5

(y-5)=-3(x-2)(y5)=3(x2)
y=-3x+6+5=-3x+11y=3x+6+5=3x+11 ->aa

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+661
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=1322, y=5/2-5y=525
x=9/2=4 1/2x=92=412, y=-5/2=-2 1/2y=52=212