SOLUTION: for the floor plans given in exercise determine whether the side through the points (2,3) and (11,6) is perpendicular to the side through the points (2,3) and (-3, 18). THE FLO

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Question 104741: for the floor plans given in exercise determine whether the side through the points (2,3) and (11,6) is perpendicular to the side through the points (2,3) and (-3, 18).
THE FLOOR PLANS IN THE GIVEN EXERCISE ARE (2,3), (11,6), (-3, 18) AND (8,21)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Line 1 is through (2,3) and (11,6).
Line 2 is through points (2,3) and (-3, 18).
For lines to be perpendicular, their slopes are negative reciprocals,
m%5B2%5D=-%281%2Fm%5B1%5D%29 or
m%5B1%5Dm%5B2%5D=-1
Let's calculate the slope of both lines and see if this relationship holds.
The formula for the slope is :
m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29
For Line 1,
m%5B1%5D=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29
m%5B1%5D=%286-3%29%2F%2811-2%29
m%5B1%5D=3%2F9
m%5B1%5D=1%2F3
For Line 2,
m%5B2%5D=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29
m%5B2%5D=%2818-3%29%2F%28-3-2%29
m%5B2%5D=-3
When we look at the product of their slopes
m%5B1%5Dm%5B2%5D=1%2F3%28-3%29=-1
We find that they are negative reciprocals and therefore the lines are perpendicular, as you can see by the graph below.