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Triangle DEF has vertices D(1, 3), E(3, –1), and F(–2, –1). Determine if triangle DEF is an equilateral, isosceles, or scalene triangle.

Aequilateral

Bisosceles

Cscalene

Dnone of these

Verified Answer :

I would say B. isosceles :)

Answer:

DEF is a isosceles triangle.

B is correct.

Step-by-step explanation:

Given The vertices of triangle D(1, 3), E(3, –1), and F(–2, –1)

We will find distance or length of each side of triangle using distance formula.

Formula:

\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

\(\text{Length DE}=\sqrt{(3-1)^2+(-1-3)^2}=\sqrt{4+16}=\sqrt{20}=2\sqrt{5}\)

\(\text{Length EF}=\sqrt{(-2-3)^2+(-1+1)^2}=\sqrt{25+0}=\sqrt{25}=5\)

\(\text{Length DF}=\sqrt{(-2-1)^2+(-1-3)^2}=\sqrt{9+16}=\sqrt{25}=5\)

Thus, EF=DF=5

If two sides of triangle is equal then it is isosceles triangle.

Hence, DEF is a isosceles triangle.