SOLUTION: In the x-y plane, points D(1,0), E(1,6), and F(r,s) are the vertices of a right triangle. If line DE is the hypotenuse of the right triangle, which of the following CANNOT be the
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Question 863831: In the x-y plane, points D(1,0), E(1,6), and F(r,s) are the vertices of a right triangle. If line DE is the hypotenuse of the right triangle, which of the following CANNOT be the area of the triangle?
**I suppose there is the inclusion of an inscribed triangle within a circle with its diameter being measured at 6 (units covered by the base - hypotenuse - of the triangle on the plane), however I do not quite understand how to go about deciphering this conundrum...
A) 0.6
B) 4.7
C) 7.5
D) 8.8
E) 9.2
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
D(1,0), E(1,6), and F(r,s)
D(1,0), E(1,6)
DE=6
a^2+b^2=c^2=6^2
We need the distances of a=DF and b=EF such that
a^2+b^2=6^2
a^2=(6-s)^2+(1-r)^2,
b^2=(0-s)^2+(1-r)^2,
a^2+b^2=36,
1/2ab=x
E)9.2 only has complex solutions with imaginary numbers
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