Mathematics: 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. a. equilateral b. isosceles c. scalene d. none of these

1.76, this is the answer according to e2020/ingenuity ...

Triangle def has vertices d(1, 3), e(3, –1), and

Zarek9344

31.12.2021

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.

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