But how do we do that? Well, like we've done in previous videos what I'm gonna do is I'm
So, let's just, instead of thinking of this in terms of rotating 270 degrees in the positive direction, in the counter-clockwise direction, let's think about, let's think about this, rotating this 90 degrees And 90 degree rotations are a little bit easier to think about. You see that that is equivalent, that is equivalent to a 90 degrees, to a 90 degrees clockwise rotation, or a negative 90 degree rotation. We're going in aĬounter-clockwise direction. If you imagine a point right over here this would be 90 degrees, 180, and then that is 270 degrees.
Negative 270 degree rotation, but if we're talking aboutĪ 270 degree rotation. In the previous video when we were rotating around the origin, if you rotate something by, last time we talked about a So, to help us think about that I've copied and pasted this on my scratch pad and we can draw through it and the first thing that we might wanna think about is if you rotate, I've talked about this So, this would be 270 degrees in the counter-clockwise direction. The direction of rotation by a positive angle is counter-clockwise. We have this little interactive graph tool where we can draw points or if we wanna put them in the trash we can put them there.
Triangle SAM, S-A-M, and this is one over here, S-A-M, is rotated 270 degrees, about the point four comma negative two. But it's easy to calibrate it if you want to specify another point, around which you want to rotate - just make that point the new origin! Figure out the other points' coordinates with respect to your new origin, do the transformations, and then translate everything back to coordinates with respect to the old origin. Now, since (a, b) are coordinates with respect to the origin, this only works if we rotate around that point. Rotating (a, b) 360° would result in the same (a, b), of course. Because the axes of the Cartesian plane are themselves at right angles, the coordinates of the image points are easily predictable: with a bit of experimentation, you could easily 'prove' to yourself that rotating (a, b) 90° would result in (-b, a) rotation of 180° gives us (-a, -b) and one of 270° would bring us to (b, -a). But points, lines, and shapes can be rotates by any point (not just the origin)! When that happens, we need to use our protractor and/or knowledge of rotations to help us find the answer.Here's my idea about doing this in a bit more 'mathematical' way: every rotation I've seen until now (in the '.about arbitrary point' exercise) has been of a multiple of 90°. The rotation rules above only apply to those being rotated about the origin (the point (0,0)) on the coordinate plane. If we compare our coordinate point for triangle ABC before and after the rotation we can see a pattern, check it out below: To derive our rotation rules, we can take a look at our first example, when we rotated triangle ABC 90º counterclockwise about the origin. Rotation Rules: Where did these rules come from? Yes, it’s memorizing but if you need more options check out numbers 1 and 2 above! Know the rotation rules mapped out below.Use a protractor and measure out the needed rotation.We can visualize the rotation or use tracing paper to map it out and rotate by hand.There are a couple of ways to do this take a look at our choices below: Let’s take a look at the difference in rotation types below and notice the different directions each rotation goes: How do we rotate a shape? Rotations are a type of transformation in geometry where we take a point, line, or shape and rotate it clockwise or counterclockwise, usually by 90º,180º, 270º, -90º, -180º, or -270º.Ī positive degree rotation runs counter clockwise and a negative degree rotation runs clockwise.