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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 = (6-3)/(11-2) = 3/9 = 1/3
For the points (-3,18) and (8,21)
m2 = (21-18)/(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 = (8-3)/(-3-2) = 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.