SOLUTION: 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)

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: 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)       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 106084: 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 perpendicular to the side through the points (2,3) and (-3,18).
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
1. the side through the points (2,3) and (11,6)
Find a slope a%5B1%5D:

a%5B1%5D = (y%5B2%5D –y%5B1%5D)/(x%5B2%5D – x%5B1%5D)
a%5B1%5D+=+%286-3%29%2F%2811-2%29
a%5B1%5D=+3%2F9
a%5B1%5D+=+1%2F3


2.
the side through the points (2,3) and (-3,18)
Find a slope a%5B2%5D:

a%5B2%5D = (y%5B2%5D –y%5B1%5D)/(x%5B2%5D – x%5B1%5D)
a%5B2%5D+=+%2818-3%29%2F%28-3-2%29
a%5B2%5D=+15%2F%28-5%29
a%5B2%5D+=+-3

If the product of slopes is equal to -1, lines are perpendicular.
We have a%5B1%5D+=1%2F3 and a%5B2%5D+=+-3,
so
a%5B1%5D%2Aa%5B2%5D+=+%281%2F3%29%2A%28-3%29
a%5B1%5D%2Aa%5B2%5D+=+-1 ............. => your lines are perpendicular