A line passes through #(6 ,4 )# and #(9 ,2 )#. A second line passes through #(3 ,1 )#. What is one other point that the second line may pass through if it is parallel to the first line?

Question

1001 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-01-14T07:38:11

another point of the second line is: #(1;7/3)#

A line parallel to another one has the same slope, then you can find the slope m of the first line by the following formula:

#m=(Deltay)/(Deltax)=(2-4)/(9-6)=-2/3#

where #Deltay# is the difference between the y-coordinates of the given points and #Deltax# is the difference between their x-coordinates.

To find another point of the second line you can choose one coordinate and find the second, depending on the chosen one:

Then if you decide, for example, to choose #color(red)(x=1)#, you would solve:

#(Deltay)/(Deltax)=(1-y)/(3-color(red)1)=-2/3#

where(3;1) is the given point of the second line.

That's

#3*(1-y)=-2*2#

#3-3y=-4#

#y=7/3#

Then another point of the second line is: #(1;7/3)#