Answer:
Option C.
Step-by-step explanation:
It is given that a rotation maps a triangle with vertices A(3,1), B(-1,-1), and C(7,-2) to A'B'C'.
We know that rotation is a rigid transformation. It means the size and shape of the figure remains same. In other words we can say that preimage and image are congruent.
[tex]\triangle ABC\cong \triangle A'B'C'[/tex]
The corresponding parts of congruent triangles are congruent.
[tex]BC\cong B'C'[/tex]
[tex]BC=B'C'[/tex]
Distance formula:
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
The distance of B(-1,-1), and C(7,-2) is
[tex]BC=\sqrt{(7-(-1))^2+(-2-(-1))^2}[/tex]
[tex]BC=\sqrt{(8)^2+(1)^2}[/tex]
[tex]BC=\sqrt{65}[/tex]
[tex]BC\approx 8.06[/tex]
Approx to the nearest unit.
[tex]BC=B'C'=8[/tex]
Therefore, the correct option is C.
