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.
