SOLUTION: Use analytic geometry to classify the quadrilateral with vertices D(10,0), E(2,4), F(-8,-6), and G(6,-8). Explain your reasoning and show all your work.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Use analytic geometry to classify the quadrilateral with vertices D(10,0), E(2,4), F(-8,-6), and G(6,-8). Explain your reasoning and show all your work.      Log On


   

Question 177776: Use analytic geometry to classify the quadrilateral with vertices D(10,0), E(2,4), F(-8,-6), and G(6,-8). Explain your reasoning and show all your work.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!

Looks like a kite.
If it is then,
DE=DG
FE=FG
Use the distance formula,
D%5E2=%28x%5B1%5D-x%5B2%5D%29%5E2%2B%28y%5B1%5D-y%5B2%5D%29%5E2
For DE,
D%5E2=%2810-2%29%5E2%2B%280-4%29%5E2
D%5E2=64%2B16
highlight%28+D=sqrt%2880%29%29%29
For DG,
D%5E2=%2810-6%29%5E2%2B%280-%28-8%29%29%5E2
D%5E2=16%2B64
highlight%28+D=sqrt%2880%29%29
.
.
.
For FE,
D%5E2=%28-8-2%29%5E2%2B%28-6-4%29%5E2
D%5E2=100%2B100
highlight%28+D=sqrt%28200%29%29
For FG,
D%5E2=%28-8-6%29%5E2%2B%28-6-%28-8%29%29%5E2
D%5E2=196%2B4
highlight%28+D=sqrt%28200%29%29
.
.
.
We have have proved that the classification is a kite because,
DE=DG
FE=FG