How do I do 90 counterclock wise rotations about the origin on points (-5,-5) , (0,-5) , (0,0)?
I don't know at what level you are working at, but if you
are into matrices, here is an excellent video that not only
develops the rotation matrix but actually uses a 90° rotation
as an example.
https://www.youtube.com/watch?v=OYuoPTRVzxY
If you don't know what a matrix is, why not just draw the points
on a graph and see where a 90° rotation puts you.
Btw, a positive rotation is counterclockwise, a concept that you
should remember from trig.
I'm not in trig yet. I'm going to 9th grade and will take geometry? (I think.. but thank you)
Just recall that such a rotation takes
(x,y) -> (-y,x)
So, (0,-5) -> (5,0)
and similarly for the other points
To perform a 90-degree counterclockwise rotation about the origin, you can follow these steps:
1. Plot the given points on a coordinate plane. In this case, the points are (-5,-5), (0,-5), and (0,0).
2. Draw lines from the origin to each of the points.
3. To rotate a point counterclockwise about the origin, swap the x and y coordinates and negate the new x-coordinate. This can be done using the following formulas:
- New x-coordinate = -y
- New y-coordinate = x
4. Apply the rotation formulas to each of the given points:
- For the point (-5,-5):
- New x-coordinate = -(-5) = 5
- New y-coordinate = -5
- The new rotated point is (5,-5).
- For the point (0,-5):
- New x-coordinate = -(-5) = 5
- New y-coordinate = 0
- The new rotated point is (5,0).
- For the point (0,0):
- New x-coordinate = -(0) = 0
- New y-coordinate = 0
- The new rotated point is (0,0).
5. Plot the new rotated points on the coordinate plane.
The final result of performing a 90-degree counterclockwise rotation about the origin on the given points (-5,-5), (0,-5), and (0,0) is (5,-5), (5,0), and (0,0), respectively.