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

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Answer 1 · 2017-01-26T10:22:02

$(4 1/2, -2 1/2)$

$6y-2x=1$
$6y=2x+1$

$y=1/3x+1/6$
The slope for this equation is $1/3$ , therefor the slope for line segment, $m =-3$ where $m*m_1=-1$

The equation of line segment is $(y-y_1)=m(x-x_1)$ where $x_1=2, y_1=5$

$(y-5)=-3(x-2)$
$y=-3x+6+5=-3x+11$ $->a$

so, the intercept between 2 lines is
$1/3x+1/6=-3x+11$

$2/6x+1/6=-3x+11$

$2x+1=6(-3x+11)$
$2x=-18x+66-1$
$20x=65$
$x = 65/20 = 13/4 =3 1/4$

therefore,
$y=-3(13/4)+11$
$y=-39/4+44/4$
$y=5/4=1 1/4$

The line which intercept with both lines is a midpoint of the line segment. Therefore the other end line $(x,y)$

$(x+2)/2=13/4$ , $(y+5)/2=5/4$

$x+2=13/2$ , $y+5=5/2$

$x=13/2-2$ , $y=5/2-5$
$x=9/2=4 1/2$ , $y=-5/2=-2 1/2$

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