Help me answer this problem
2 answers:
You might be interested in
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.
Step-by-step explanation:
Given
To get g(x), we will have to integrate g'(x)
If g(1) = 0, this means at x = 1, g(x) = 0
0 = -1⁻¹ + C
C= 1
Substitute C = 1 into the function
g(x) = -x⁻¹ + 1
If g(2) = 0, this means at x = 2, g(x) = 0
0 = -2⁻¹ + C
C= 2⁻¹
C = 1/2
Substitute C = 2 into the function
g(x) = -x⁻¹ + 1/2