A line passes through (2 ,9 )(2,9) and (5 ,6 )(5,6). A second line passes through (3 ,8 )(3,8). What is one other point that the second line may pass through if it is parallel to the first line?

1 Answer
Alan P.
May 14, 2016

(1,10)(1,10) would be one possible other point

Explanation:

The line through (2,9)(2,9) and (5,6)(5,6) has a slope of
color(white)("XXX")m=(9-6)/(2-5) = -1XXXm=9−62−5=−1
or expressed in another way the slope ratio is
color(white)("XXX")Deltay:Deltax=-1:1

Any parallel line will also have this same slope ratio.

If a line passes through (3,8) with a slope ratio of -1:1
then points on the line will have the form: (3+k,8-k) for a constant k.

Picking an arbitrary value of k
color(white)("XXX")k=-2
would give the point (3-2,8-(-2))=(1,10)

Related questions
See all questions in Equations of Parallel and Perpendicular Lines
Impact of this question
1431 views around the world
You can reuse this answer
Creative Commons License