Answer:
(x, y) ⇒ (-x, -y)
Step-by-step explanation:
There are a couple of ways you can go at this.
1) Rotation by 180° in either direction is the same as reflection across the origin. That reflection is identical to reflection across both the x- and y-axes, in either order, so negates both coordinates. The transformation rule is ...
(x, y) ⇒ (-x, -y)
__
2) The rule for a general rotation by angle α is ...
(x, y) ⇒ (x·cos(α) -y·sin(α), x·sin(α) +y·cos(α))
For α = 180°, sin(α) = 0 and cos(α) = -1. This makes the rule for rotation by 180° be ...
(x, y) ⇒ (-x, -y)
Answer:
To find a a fraction of a whole number, you multiply the numerator of the fraction by the given number and then divide the product by the denominator of the fraction
Solved example for finding a fraction of a whole number:
1)
Find 1/3 of 21.
To find 1/3 of 21, we multiply the numerator 1 by the given whole number 21 and then divide the product 21 by the denominator 3.
1/3 × 21 = 1 × 21/3 = 21/3 = 7
So, 1/3 of 21 = 7.
1/3 of 21 is 7
This happens whenever
or
. More generally,
whenever you start with one of these angles and add any multiple of
, so the general solution would be
, where
is any integer. (Notice that when
, you end up with
.)
