A line segment is bisected by a line with the equation $4 y - 3 x = 2$ . If one end of the line segment is at $( 2 , 1 )$ , where is the other end?

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Answer 1 · 2017-01-24T17:20:56

$(1 1/25,2 7/25)$

$4y-3x=2$ , $4y=3x+2$
$y=3/4x+1/2$ $->a$

gradient of the other line, $m = -1/(3/4)=-4/3$

The equation of the line thru $(2,1)$ ,

$y-y_1=m(x-x_1)$
$y-1=-4/3(x-2)$
$y=-4/3x+8/3+1$
$y=-4/3x+11/3$

replacing y from $a$

$3/4x+1/2=-4/3x+11/3$

$3/4x+4/3x=11/3-1/2$

$9/12x+16/12x=22/6-3/6$

$25/12x=19/6$

$x=19/6*12/25=38/25$

$y=3/4(38/25)+1/2$

$y=57/50+25/50=82/50=41/25$

$(38/25,41/25)$ is a midpoint of the line.

The other end of the line, $(x,y)$ .

$(x+2)/2=38/25$
$x=38/25*2-2$
$x=76/25-50/25=26/25=1 1/25$

$(y+1)/2=41/25$
$y=41/25*2-1$
$y=82/25-25/25=57/25=2 7/25$

The other end $(1 1/25,2 7/25)$

A line segment is bisected by a line with the equation 4 y - 3 x = 2 4 y - 3 x = 2 . If one end of the line segment is at ( 2 , 1 )( 2 , 1 ), where is the other end?