A line passes through #(5 ,1 )# and #(6 ,5 )#. A second line passes through #(1 ,3 )#. What is one other point that the second line may pass through if it is parallel to the first line?

1 Answer
Alan P.
Jul 13, 2016

One other point that satisfies these conditions is #(2,8)#

Explanation:

The slope of a line through #(5,1)# and #(6,5)#
is #(Deltay)/(Deltax)=(5-1)/(6-5)=5/1#

A line through#(1,3)# parallel to this first line must have the same slope.

As long as the ratio #Deltay:Deltax# is maintained
#(1+Deltax,3+Deltay)# will be a valid point on this second line.

Some possibilities that maintain this ratio:
#color(white)("XXX")(Deltax,Deltay)=(1,5)color(white)("XX")rarrcolor(white)("XX")"point:"(1+1,3+5)=(2,8)#

#color(white)("XXX")(Deltax,Deltay)=(2,10)color(white)("XX")rarrcolor(white)("XX")"point:"(1+2,3+10)=(3,11)#

#color(white)("XXX")(Deltax,Deltay)=(-1,-5)color(white)("XX")rarrcolor(white)("XX")"point:"(1+(-1)1,3+(-5))=(0,2)#

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