A line segment is bisected by a line with the equation $- 3 y + 4 x = 6$ . If one end of the line segment is at $( 3 , 1 )$ , where is the other end?

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A line segment is bisected by a line with the equation $- 3 y + 4 x = 6$ . If one end of the line segment is at $( 3 , 1 )$ , where is the other end?

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Answer 1 · 2017-06-21T09:58:48

The other end is $=(51/25,129/75)$

Explanation:

Let the other end be $(x,y)$

Then the mid-point of the line is $=((x+3)/2, (y+1)/2)$

The slope of the line $-3y+4x=6$ ............ $(1)$

is

$=4/3$

The slope of the line perpendicular is

$=-3/4$

The equation of the line is

$-3/4(x-3)=(y-1)$

$-3x+9=4y-4$

$4y+3x=13$ ............. $(2)$

Solving for $x$ and $y$ , in equations $(1)$ and $(2)$

$4x-3*(13-3x)/4=6$

$16x-39+9x=24$

$25x=24+39=63$

$x=63/25$

$y=1/3*(4*63/25-6)$

$=102/75$

The mid-point is $=(63/25,102/75)$

So,

$(x+3)/2=63/25$

$x=126/25-3=51/25$

$(y+1)/2=102/75$

$y=204/75-1=129/75$

The other end is $=(51/25,129/75)$

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A line segment is bisected by a line with the equation $- 3 y + 4 x = 6$ . If one end of the line segment is at $( 3 , 1 )$ , where is the other end?

1 Answer

Explanation:

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Science

Math

Humanities

... and beyond

A line segment is bisected by a line with the equation - 3 y + 4 x = 6 - 3 y + 4 x = 6 . If one end of the line segment is at ( 3 , 1 )( 3 , 1 ), 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 $- 3 y + 4 x = 6$ . If one end of the line segment is at $( 3 , 1 )$ , where is the other end?