SOLUTION: determine if this quadrilateral with the given vertices is a square A(1,-2) B(4,2) C(6,2) D(3,-2)

Algebra ->  Rectangles -> SOLUTION: determine if this quadrilateral with the given vertices is a square A(1,-2) B(4,2) C(6,2) D(3,-2)      Log On


   

Question 1136913: determine if this quadrilateral with the given vertices is a square
A(1,-2) B(4,2) C(6,2) D(3,-2)
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
A(1,-2) B(4,2) C(6,2) D(3,-2)
use distance formula to find out if distances AB, CD,AD, and BC are same; if yes than this quadrilateral with the given vertices is a square
AB
Solved by pluggable solver: Distance Between 2 points
The distance formula is sqrt%28%28%28x%5B2%5D-x%5B1%5D%29%5E2%29%2B%28%28y%5B2%5D-y%5B1%5D%29%5E2%29%29. Plug in the numbers,
sqrt%28%28%284-%281%29%29%5E2%29%2B%28%282-%28-2%29%29%5E2%29%29
sqrt%283%5E2%2B4%5E2%29 The distance is 5.



CD
Solved by pluggable solver: Distance Between 2 points
The distance formula is sqrt%28%28%28x%5B2%5D-x%5B1%5D%29%5E2%29%2B%28%28y%5B2%5D-y%5B1%5D%29%5E2%29%29. Plug in the numbers,
sqrt%28%28%283-%286%29%29%5E2%29%2B%28%28-2-%282%29%29%5E2%29%29
sqrt%28-3%5E2%2B-4%5E2%29 The distance is 5.




AD
Solved by pluggable solver: Distance Between 2 points
The distance formula is sqrt%28%28%28x%5B2%5D-x%5B1%5D%29%5E2%29%2B%28%28y%5B2%5D-y%5B1%5D%29%5E2%29%29. Plug in the numbers,
sqrt%28%28%283-%281%29%29%5E2%29%2B%28%28-2-%28-2%29%29%5E2%29%29
sqrt%282%5E2%2B0%5E2%29 The distance is 2.



BC
Solved by pluggable solver: Distance Between 2 points
The distance formula is sqrt%28%28%28x%5B2%5D-x%5B1%5D%29%5E2%29%2B%28%28y%5B2%5D-y%5B1%5D%29%5E2%29%29. Plug in the numbers,
sqrt%28%28%284-%286%29%29%5E2%29%2B%28%282-%282%29%29%5E2%29%29
sqrt%28-2%5E2%2B0%5E2%29 The distance is 2.




this quadrilateral with the given vertices is not a square