A line passes through #(8 ,2 )# and #(6 ,7 )#. A second line passes through #(3 ,8 )#. What is one other point that the second line may pass through if it is parallel to the first line?

1 Answer
Jul 21, 2017

Infinite points given by #(a,(31-5a)/2)#

Explanation:

As the first line passes through #(8,2)# and #(6,7)# its slope is

#(7-2)/(6-8)=-5/2#

Let the other point be #(a,b)# and as line joining #(a,b)# and #(3,8)# is parallel to first line, it will too have a slope of #-5/2#

Hence #(b-8)/(a-3)=-5/2#

or #2b-16=-5a+15#

i.e. #2b=-5a+31#

or #b=(31-5a)/2#

Hence the point #(a,(31-5a)/2)# is the other point.

Observe that by changing various values of #a#, we can have many points and hence therecould be infinite points. For example if #a=-3#, the point is #(-3,23)#.

graph{((x-8)^2+(y-2)^2-0.02)((x-6)^2+(y-7)^2-0.02)((x-3)^2+(y-8)^2-0.02)(5x+2y-31)(5x+2y-44)=0 [-6.38, 13.62, 0, 10]}