Answer:
i) A. 180º rotation about the origin, ii) 
.
Step-by-step explanation:
i) In this case, we understand that vertex 
changed to 
after doing an operation. At first we must calculate the distance of each point regarding origin by Pythagorean Theorem:
Point P:
If we know that 
, 
, 
and 
, the distance 
is:
Point P':
If we know that 
, 
, and , the distance 
is:
As 
, origin is the center of rotation.
Besides, 
is a multiple of 
, that is:
1) 
Given
2) 
3) 
Scalar multiplication of a vector/Result.
The value of the scalar proves that P experimented a 180º rotation about the origin. Hence, the correct answer is A.
ii) If 
and the same operation described in item i) is used, then, the location of 
is:
Which corresponds to option C.
