Switch the coordinates and change the sign of the second one by multiplying it by negative 1.
Here are some examples and a more general way to understand the problem.
Consider the point (1,1), a 90 degree rotation clockwise about the origin would move it into the 4th quadrant.
The new point is (1,-1) , similarly (-4,2)-> (2,4), (-4,3)-> (3,4)
We take a point p= (x,y) the the result of rotation p 90 clockwise about the orgin is a new point p'=(x',y')= (-y, x). .
In the case of p=(1,0) the new point is p'= (0, -1)
One can use a matrix where the first row is cos(a), sin(a) and the second row is
-sin(a) cos(a) for any clockwise rotation of a degrees about the origin.
If we let a=90 degrees we have
[0 1] as the first row and [-1 0] as the second row. So the matrix is:
|0 1|
|-1 0|
Call that matrix M
So a point p= (x,y) can be multiplied by M as follows Mp=p' where p' is the rotated point.
If p=(-4,2) then Mp
is M(-4,2) which after matrix multiplication means x'=0*-4+1*2=2 and y'=-1*-4+0*2=4
So p'=(2,4)
Try it with (1,0)
x'=1*0+0*1=0
y'=-1*1+0*1=-1
so p'=(0,-1) and (1,0)->(0,-1)
How about the point on the y axis (0,1), it should go to the point (1,0)
0*1+1*1=1 and -1*0+0*1 gives you the pont (1,0) ( we don't see the negative sign because -0 is just 0)
You dont, its just 90 degrees 3 times..
Move it 3 times* * * * *or once in the anti-clockwise direction.
To rotate a figure 180 degrees clockwise about the origin you need to take all of the coordinates of the figure and change the sign of the x-coordinates to the opposite sign(positive to negative or negative to positive). You then do the same with the y-coordinates and plot the resulting coordinates to get your rotated figure.
rotate it 90 degrees
I dont really know if this is right but i think to do this problem you have to take a point then rotate the paper counter clockwise around the origin then you have a new point which is called a prime. Then reflect it over the y axis on the graph.
You dont, its just 90 degrees 3 times..
Move it 3 times* * * * *or once in the anti-clockwise direction.
To rotate a figure 180 degrees clockwise about the origin you need to take all of the coordinates of the figure and change the sign of the x-coordinates to the opposite sign(positive to negative or negative to positive). You then do the same with the y-coordinates and plot the resulting coordinates to get your rotated figure.
No, only their positions will change.
Take any one point on the figure. Draw a line from it to the origin. At the origin measure an angle of 90 degrees (right angle) in a clockwise direction. Draw a line from the origin at this new angle and of the same length as the original angle. Repeat this process for the other points in the figure. NB Be careful, there will be numerous lines from the origin. At the end points of the new lines, connect up to reveal the origin figure ,but rotated 90 degrees - clockwise.
multiply the coordinates by -1.
rotate it 90 degrees
I dont really know if this is right but i think to do this problem you have to take a point then rotate the paper counter clockwise around the origin then you have a new point which is called a prime. Then reflect it over the y axis on the graph.
360 degree rotation (clockwise or anticlockwise) leaves any figure in exactly the same position as it was at the start. So YOU DO NOTHING.
Visualize a capital "N." Rotated 90 degrees counter-clockwise (a quarter turn to the left) it would look like a capital "Z."
The x,y origin is 0,0
The same as 180 degrees clockwise. What do you mean "the answer to"?