Question

The coordinates of the vertices of A DEF are D(-4,1), E(3. – 1), and F(-1, – 4)

Answer 1

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 $\sqrt{(-4-3)^{2}+(1-(-1))^{2} } =\sqrt{53}$ units

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

and length of FD is given by $\sqrt{(-4-(-1))^{2}+(1-(-4))^{2} } =\sqrt{34}$ 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)