A line passes through #(8 ,5 )# and #(6 ,4 )#. A second line passes through #(3 ,5 )#. What is one other point that the second line may pass through if it is parallel to the first line?

1 Answer
Shwetank Mauria
Sep 22, 2016

Any point other than #(7,6)# and satisfying the condition #x-2y+7=0# could be such a point. Examples are #(-5,1)#, #(7,7)# and #(-1,3)#.

Explanation:

A line passing through #(x_1, y_1)# and #(x_2, y_2)# has a slope of #(y_2-y_1)/(x_2-x_1)#. Hence slope of line joining #(8,5)# and #(6,4)# is

#(4-5)/(6-8)=(-1)/(-2)=1/2#

As the second line passing through #(3,5)# is parallel to the above, its slope too is #1/2#.

Now, equation of a line passing through #(x_1,y_1)# and having a slope of #m# is #(y-y_1)=m(x-x_1)#. Hence, the equation of line passing through #(3,5)# and having a slope of #1/2# is

#(y-5)=1/2(x-3)# or #2y-10=x-3# i.e. #x-2y+7=0#

Hence, any point satisfying the condition #x-2y+7=0# (other than #(3,5)# will satisfy this.

Let #x=-5# then #y=1#, hence point could be #(-5,1)# or

let #x=7# then #y=7#, hence other point could be #(7,7)# or

let #x=-1# then #y=3#, hence point could be #(-1,3)#

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