Answer:
Furthermore, it turns out that rotations by 180^\circ180
∘
180, degrees or -90^\circ−90
∘
minus, 90, degrees follow similar patterns:
R_{(0,0),180^\circ}(\tealD{x},\purpleC{y})=(-\tealD{x},-\purpleC{y})R
(0,0),180
∘
(x,y)=(−x,−y)R, start subscript, left parenthesis, 0, comma, 0, right parenthesis, comma, 180, degrees, end subscript, left parenthesis, start color #01a995, x, end color #01a995, comma, start color #aa87ff, y, end color #aa87ff, right parenthesis, equals, left parenthesis, minus, start color #01a995, x, end color #01a995, comma, minus, start color #aa87ff, y, end color #aa87ff, right parenthesis
R_{(0,0),-90^\circ}(\tealD{x},\purpleC{y})=(\purpleC{y},-\tealD{x})R
(0,0),−90
∘
(x,y)=(y,−x)R, start subscript, left parenthesis, 0, comma, 0, right parenthesis, comma, minus, 90, degrees, end subscript, left parenthesis, start color #01a995, x, end color #01a995, comma, start color #aa87ff, y, end color #aa87ff, right parenthesis, equals, left parenthesis, start color #aa87ff, y, end color #aa87ff, comma, minus, start color #01a995, x, end color #01a995, right parenthesis
We can use these to rotate any point we want by plugging its coordinates in the appropriate equation.
Step-by-step explanation:
Step-by-step explanation:
the same "conversion process" applies.
whatever expression was in place of the old x gets a negative sign and moves into the spot of y.
and whatever expression was in place of the old y moves into the spot of x.
so, in general, we could say
the original is (f(x), g(y)).
and the 90° rotation is then
(f(x), g(y)) -> (g(y), -f(x))
add on : that means, of course, that if the old x was already a negative number, it turns via "--" into a positive number for the new y.
last but not least : we are talking here about a 90° clockwise rotation. right?
because for the counterclockwise rotation it is
(f(x), g(y)) -> (-g(y), f(x))
