A line passes through #(9 ,2 )# and #( 4, 5 )#. A second line passes through #( 4, 1 )#. What is one other point that the second line may pass through if it is parallel to the first line?

Question

1892 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-02-13T08:36:15

#(-6,7)#

Two parallel lines have the same gradient.

When we calculate the gradient of the first line,

gradient = #(y_2-y_1)/(x_2-x_1)#

#(5-2)/(4-9)=-3/5#

The gradient of the second line will also be #-3/5#
We already have the coordinates #(4,1)# for the second line,

Now let's say that it passes through the point #(x_2,y_2).#
We can take #y_2= 7.#

This is to simplify later, we can take any number for #y_2# because there are infinitely many points on the line.

So
gradient = #-3/5# = #(7-1)/(x_2-4)#

#5(7-1) = -3(x_2-4)#

#30=-3x_2+12#

#30-12=-3x_2#

#x_2=18/-3#

#x_2 =-6#

So the coordinates of a second point are #(-6,7)#