Question

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

Answer 1

I would say B. isosceles :)

Answer 2

DEF is a isosceles triangle.

B is correct.

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=√((x_2-x_1)^2+(y_2-y_1)^2)`

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

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

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

Thus, EF=DF=5

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

Hence, DEF is a isosceles triangle.