The question is incomplete. Here is the complete question:
The triangle will be rotated 180° clockwise around the point (3, 4) to create A A'B'C.Which
characteristics of AA'B'C' will be the same for the corresponding characteristics of AABC? Select ALL that apply.
(A) The coordinates of A'.
(B) The coordinates of B'.
(C) The perimeter of Δ A'B'C'.
(D) The area of Δ A'B'C'.
(E) The measure of ∠B'.
(F) The length of segment A'B'.
Answer:
(C) The perimeter of Δ A'B'C'.
(D) The area of Δ A'B'C'.
(E) The measure of ∠B'.
(F) The length of segment A'B'.
Step-by-step explanation:
Given:
A triangle ABC rotated by 180° clockwise around the vertex C(3,4) to create Δ A'B'C.
Now, a rotation is a rigid motion transformation. In rigid transformation, the size, length, angle measures, perimeter and area of the figure doesn't change and remains the same as the original figure.
Rotation only changes the position of the points on the figure.
Here, as the triangle ABC is rotated about vertex C, the position of vertex A and B will change. But, the angles made by each of the vertices will remain same. Also, the side lengths of the triangle will remain the same. So, the perimeter and area will also not change. As the point of rotation is point C, the vertex C' will be same as vertex C.
So, the correct options are (C), (D), (E), and (F).
