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?

Question

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?

1 Answer

Impact of this question

1995 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-01-26T10:22:02

$(4 \frac{1}{2}, - 2 \frac{1}{2})$ $(4 1/2, -2 1/2)$

Explanation:

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

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

The equation of line segment is $(y - y_{1}) = m (x - x_{1})$ $(y-y_1)=m(x-x_1)$ where $x_{1} = 2, y_{1} = 5$ $x_1=2, y_1=5$

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

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

$\frac{2}{6} x + \frac{1}{6} = - 3 x + 11$ $2/6x+1/6=-3x+11$

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

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

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

$\frac{x + 2}{2} = \frac{13}{4}$ $(x+2)/2=13/4$ , $\frac{y + 5}{2} = \frac{5}{4}$ $(y+5)/2=5/4$

$x + 2 = \frac{13}{2}$ $x+2=13/2$ , $y + 5 = \frac{5}{2}$ $y+5=5/2$

$x = \frac{13}{2} - 2$ $x=13/2-2$ , $y = \frac{5}{2} - 5$ $y=5/2-5$
$x = \frac{9}{2} = 4 \frac{1}{2}$ $x=9/2=4 1/2$ , $y = - \frac{5}{2} = - 2 \frac{1}{2}$ $y=-5/2=-2 1/2$

Science

Math

Humanities

... and beyond

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?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

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

1 Answer

Explanation:

Related questions

Impact of this question

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?