A line segment is bisected by a line with the equation # - 9 y + 4 x = 6 #. If one end of the line segment is at #( 7 , 1 )#, where is the other end?

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Answer 1 · 2016-05-27T16:39:37

The coordinate of any point on the straight line represented by equation #4x-9y+7=0# ,will be the coordinate of other end point.

The coordinate of one end of the given line segment is (7,1).
Let the coordinate of other end be (h,k).

Hence the coordinate of its middle point is #((h+7)/2,(k+1)/2)#

The given line having equation #4x-9y=6........(1)# bisects the line segment.

So the mid point of the line segment is lying on the given straight line.
Hence its coordinate will satisfy the given equation.

So inserting #(x=(h+7)/2 and y=(k+1)/2)# in the given equation we have

#4xx(h+7)/2-9xx(k+1)/2=6#

#=>4h+28-9k-9=12#

#=>4h-9k+7=0#

Inserting x for h and y for k we get an equation of the straight line

as #4x-9y+7=0......(2)# which is a straight line parallel to the straight line represented by equation (1)

Hence the coordinate of any point on the straight line represented by equation #4x-9y+7=0......(2)# will be the coordinate of other end point.

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