Answer:
Option C is the answer.
Step-by-step explanation:
A triangle is given with vertices as D(7,3) E(8,1) and F(4,-1).
Now side DE = [tex]\sqrt{(7-8)^{2}+(3-1)^{2}[/tex]
=[tex]\sqrt{1^{2}+2^{2}}=\sqrt{1+4}=\sqrt{5}[/tex]
Side EF =[tex]\sqrt{(8-4)^{2} +(1+1)^{2} } = \sqrt{4^{2}+2^{2} }[/tex]
= [tex]\sqrt{16+4}= \sqrt{20}[/tex]
Side DF =[tex]\sqrt{(7-4)^{2}+(3+1)^{2} } = \sqrt{3^{2}+4^{2}}[/tex]
[tex]=\sqrt{16+9} = \sqrt{25}[/tex]
Now for right angle triangle
DF²≡ EF² + DE²
[tex](\sqrt{5})^{2} + (\sqrt{20})^{2}= 5^{2}[/tex]
25 = 25
Therefore, the given triangle is a right angle triangle.
Option C is the answer.
