## 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)#

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