
Perpendicular Lines
1. Geometry. Floor plans for a building have the four corners of a room located at the points (2, 3), (11, 6), (3, 18), and (8, 21). Determine whether the side through the points (2, 3) and (11, 6) is parallel to the side through the points (3, 18) and (8, 21).
For the floor plans given in #1, determine whether the sidethrough the points (2, 3) and (11, 6) is perpendicular to the side through the points
(2, 3) and (3, 18).

Parallel vs. Perpendicular:
Both involve slopes, and the rules are as follows:
If two lines (slopes) are parallel, then they are congruent (equal). In other words, if the slopes of the lines are m1 and m2:
m1 = m2
If two lines (slopes) are perpenducular, then they are oposite reciprocals of each other. In other words, for m1 and m2:
m1 = 1/m2
Therefore, all we need to do is find the slopes between the points you specified and see if the slopes match up to the rules above.
Slope is m = (y2  y1)/(x2  x1)
1)
For the points (2,3) and (11,6)
m1 = (63)/(112) = 3/9 = 1/3
For the points (3,18) and (8,21)
m2 = (2118)/(8(3)) = 3/(8+3) = 3/11
m1 does not equal m2 since 1/3 does not equal 3/11. The two slopes are not parallel.
2)
For the points (2,3) and (11,6) (same as above)
m1= 1/3
For the points (2,3) and (3,8)
m2 = (83)/(32) = 5/(1) = 5
m1 does not equal 1/m2 since 1/3 does not equal (1)/(5) [Note: m2 would have to equal 3 or m1 would have to equal +1/5 for the two angles to be perpedicular]. The two slopes are not perpendicular.