A line segment is bisected by a line with the equation $- 5 y + 2 x = 1$ . If one end of the line segment is at $(6 ,4 )$ , where is the other end?

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A line segment is bisected by a line with the equation $- 5 y + 2 x = 1$ . If one end of the line segment is at $(6 ,4 )$ , where is the other end?

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Answer 1 · 2017-07-14T08:24:25

The coordinates of the other end is $=(210/29,28/29)$

Explanation:

The equation of the line is

$-5y+2x=1$

$5y=2x-1$

$y=2/5x-1/5$ ....................... $(1)$

The slope of the line is $m=2/5$

The slope of the segment is $m'$

$mm'=-1$

$m'=-5/2$

The equation of the segment is

$y-4=-5/2(x-6)$

$y=-5/2x+15+4$

$y=-5/2x+19$ ....................... $(2)$

Solving for $x$ and $y$ in the equations $(1)$ and $(2)$ gives the point of intersection of the line and the segment

$-5/2x+19=2/5x-1/5$

$2/5x+5/2x=19+1/5$

$29/10x=96/5$

$x=96/5*10/29=192/29$

$y=2/5*192/29-1/5=71/29$

Let the other end of the segment be $=(a,b)$

Therefore,

$(192/29,71/29)=((a+6)/2,(b+4)/2)$

$(a+6)/2=192/29$

$a=384/29-6=210/29$

$(b+4)/2=71/29$

$b=144/29-4=28/29$

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A line segment is bisected by a line with the equation $- 5 y + 2 x = 1$ . If one end of the line segment is at $(6 ,4 )$ , where is the other end?

1 Answer

Explanation:

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Impact of this question

Science

Math

Humanities

... and beyond

A line segment is bisected by a line with the equation - 5 y + 2 x = 1 - 5 y + 2 x = 1 . If one end of the line segment is at (6 ,4 )(6 ,4 ), where is the other end?

1 Answer

Explanation:

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Impact of this question

A line segment is bisected by a line with the equation $- 5 y + 2 x = 1$ . If one end of the line segment is at $(6 ,4 )$ , where is the other end?