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A line passes through #(3 ,2 )# and #(1 ,3 )#. A second line passes through #(1 , 4 )#. What is one other point that the second line may pass through if it is parallel to the first line?

Question

A line passes through #(3 ,2 )# and #(1 ,3 )#. A second line passes through #(1 , 4 )#. What is one other point that the second line may pass through if it is parallel to the first line?
A line passes through #(3 ,2 )# and #(1 ,3 )#. A second line passes through #(1 , 4 )#. What is one other point that the second line may pass through if it is parallel to the first line?

Answers

One such point would be #(3,3)#

Explanation:

The line, #L_1#, through #(3,2)# and #(1,3)# has a slope of
#color(white)("XXX")m_(L1) = (Deltay_(L1))/(Deltax_(L1))=(3-2)/(1-3)=-1/2#

The line, #L_2#, through #(color(green)(1),color(magenta)4)# must have the same slope if it is parallel to #L_1#;
that is the ratio #(Deltay_(L2)):(Deltax_(L2))# must be #color(red)((-1)k):color(blue)(2k)#

and any point on #L_2# must have the form:
#color(white)("XXX")(color(green)1+color(blue)(2 * k),color(magenta)4+color(red)((-1) * k))#

For an example of such a point, we could set #k=1#
to get the point:
#color(white)("XXX")(3,3)#

enter image source here


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