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?

Question

1288 views around the world

You can reuse this answer
Creative Commons License

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]}