Answer:
m∠DEF is 90°
Step-by-step explanation:
It is given that D(5, 7), E(4, 3), and F(8, 2) form the vertices of a triangle. Thus, using the distance formula, we have
\(DE=\sqrt{(3-7)^2+(4-5)^2}\)
⇒\(DE=\sqrt{16+1}\)
⇒\(DE=\sqrt{17}\)
and \(EF=\sqrt{(2-3)^2+(8-4)^2}\)
⇒\(EF=\sqrt{1+16}\)
⇒\(EF=\sqrt{17}\)
Also, \(DF=\sqrt{(2-7)^2+(8-6)^2}\)
⇒\(DF=\sqrt{25+9}\)
⇒\(DF=\sqrt{34}\)
Now, \((DF)^2=(DE)^2+(EF)^2\)
⇒\((\sqrt{34})^2=(\sqrt{17})^2+(\sqrt{17})^2\)
⇒\(34=34\)
Thus, Pythagoras theorem holds.
Hence, m∠DEF is 90°⇒ΔDEF is right angled triangle which is right angled at E.
