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?

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Answer 1 · 2016-04-07T08:52:23

The other point is #(5, 6)#

Slope is equal to slope

Let #A(8, 5)# and #B(6, 4)# and #C(3, 5)#
Let #D(x, y)# the unknown point

slope A to B = slope D to C

#(5-4)/(8-6)=(y-5)/(x-3)#
#x-2y=-7" "# first equation

slope B to C = slope A to D
#(y-5)/(x-8)=(5-4)/(3-6)#
#x+3y=23" "#second equation

Simultaneous solution of first and second equations results to
#D(x, y)=(5, 6)#

God bless....I hope the explanation is useful.