Question

270°: (x, y)→(y, -x)
guided practice
rotate the point (-5, 2) 180° about the point (1, 4).
step 1: map the center of rotation to the origin.
the center of rotation is (1, 4)
to map (1, 4)→(0, 0), the rule is:
(x, y)→(x - 1, x - 4)
translate the point (-5, 2) using the rule (x, y)→(x - 1, y - 4).
(-5 - 1, 2 - 4)=(-6, -2)
step 3: map the center of rotation back to its original position.
this will be the ______________ of the vector in step 1.
vector from step 1: (x - 1, y - 4)
the opposite of this vector is (x + 1, y + 4)

Explanation:

Step1: Analyze the vector operation

In step 1, a vector transformation was used to map the center - of - rotation to the origin. To reverse this and map the center of rotation back to its original position, we need the opposite vector.

Step2: Recall vector properties

The opposite of a vector $(a,b)$ is $(-a,-b)$. Since the vector in step 1 was $(x - 1,y - 4)$, its opposite is $(x+1,y + 4)$.

Answer:

opposite