How do you determine if the lines through the given points (4,6), (5,3) are parallel and which, if any, are perpendicular?

Question

1332 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-11-16T18:44:00

Please see the explanation.

In general, a line is parallel to another line, if the two lines have the same slope:

#n = m#

A line will be perpendicular to another line if the slope, n of the perpendicular line has the following relationship to the slope, m:

#n = -1/m#

The slope of a line between the two points is:

#m = (3 - 6)/(5 - 4) = -3#

If a line is parallel to the line between these two points, its slope will be #-3#.

If the line is perpendicular, its slope is #1/3#