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The coordinates of the vertices of A DEF are D(-4,1), E(3. – 1), and F(-1, – 4)
Which statement correctly describes whether A DEF is a right triangle?
O
A DEF is not a right triangle because no two sides are perpendicular.
A DEF is a right triangle because DE is perpendicular to EF
A DEF is a right triangle because DF is perpendicular to EF
A DEF is a right triangle because DE is perpendicular to DF

Respuesta :

Answer:

ΔDEF is not a right triangle because no two sides are perpendicular.

Step-by-step explanation:

The coordinates of the vertices of ΔDEF are given to be D(-4,1), E(3,-1) and F(-1,-4).

Now length of DE is given by [tex]\sqrt{(-4-3)^{2}+(1-(-1))^{2}  } =\sqrt{53}[/tex] units

length of EF is given by [tex]\sqrt{(3-(-1))^{2}+(-1-(-4))^{2}  }=\sqrt{25}[/tex] units

and length of FD is given by [tex]\sqrt{(-4-(-1))^{2}+(1-(-4))^{2}  } =\sqrt{34}[/tex] units.

Therefore, 53 ≠ 25+34

Hence, the length of the sides does not support the Pythagoras theorem.

So, ΔDEF is not a right triangle because no two sides are perpendicular. (Answer)

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