A line passes through #(0 ,5 )# and #(8 ,3 )#. A second line passes through #(7 ,1 )#. What is one other point that the second line may pass through if it is parallel to the first line?

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Answer 1 · 2017-04-08T06:06:07

One such point is #(11,0)#

Let this point be #(a,b)#.

As the slope of line joining #(0,5)# and #(8,3)# is

#(3-5)/(8-0)=-2/8=-1/4#

and the slope of line joining #(7,1)# and #(a,b)# should also be the same i.e.

#(b-1)/(a-7)=-1/4#

or #4b-4=-a+7#

or #a=11-4b#

Hence any line joining a point #(11-4b,b)# with #(7,1)# will be parallel to line joining #(0,5)# and #(8,3)#

Let #b=0#, then the point is #(11,0)#

graph{(x+4y-20)(x+4y-11)=0 [-8, 12, -0.8, 9.2]}