SOLUTION: Show that the points D(-1,-2),E(2,1) and F(-3,6) are the vertices of a right triangle.

Algebra ->  Linear-equations -> SOLUTION: Show that the points D(-1,-2),E(2,1) and F(-3,6) are the vertices of a right triangle.      Log On


   

Question 157680: Show that the points D(-1,-2),E(2,1) and F(-3,6) are the vertices of a right triangle.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let's plot the points first.

It looks like a right triangle.
If the triangle is a right triangle, then the sum of the squares of the legs (DE and EF) equals the square of the hypotenuse (DF).
DF%5E2=DE%5E2%2BEF%5E2
Let's calculate the lengths of each side and test it.
The distance formula is
D%5E2=%28x%5B1%5D-x%5B2%5D%29%5E2%2B%28y%5B1%5D-y%5B2%5D%29%5E2
.
.
EF%5E2=%282-%28-3%29%29%5E2%2B%281-6%29%5E2
EF%5E2=%285%29%5E2%2B%28-5%29%5E2
EF%5E2=25%2B25
EF%5E2=50
.
.
DE%5E2=%28-1-2%29%5E2%2B%28-2-1%29%5E2
DE%5E2=%283%29%5E2%2B%28-3%29%5E2
DE%5E2=9%2B9
DE%5E2=18
.
.
DF%5E2=%28-1-%28-3%29%29%5E2%2B%28-2-6%29%5E2
DF%5E2=%282%29%5E2%2B%28-8%29%5E2
DF%5E2=4%2B64
DF%5E2=68
.
.
DF%5E2=DE%5E2%2BEF%5E2
68=18%2B50
68=68
True, therefore the triangle is a right triangle.