In the clockwise direction well, then this is gonna go four in this direction just like that. So, if you were to rotate this, the entire triangle 90 degrees Let me make this clear, this side that I'm highlighting in green which we see are four units long. One, two, three, four, five, six, seven, it's gonna put us right over here. One is one, two, three, four, five, six, seven units long, so it's still gonna be seven units long. It is going to end up, it is going to end up pointing up and how long is it going to be? Well, let's see, this To each of these sides? Well, this side right over here, if I rotate it by negative 90 degrees it is going to end up, Rotating this right triangle, this magenta one that I just constructed, by negative 90 degrees,īy negative 90 degrees, or 90 degrees in the clockwise direction. All right, so I have this right triangle. So, it's gonna go, it's gonna be, like, it's gonna look like that, and then it's gonna look like, whoops, that wasn't to press my, Of the right triangles is gonna be the line Trouble switching color, point M right over here, and I'm gonna construct a right triangle between point M and our center of rotation where the hypotenuse Gonna take each point, let's say point, using 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). To fully describe a rotation, it is necessary to specify the angle of rotation, the direction, and the point it has been rotated about.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°. To understand rotations, a good understanding of angles and rotational symmetry can be helpful. or anti-clockwise close anti-clockwise Travelling in the opposite direction to the hands on a clock. Rotations can be clockwise close clockwise Travelling in the same direction as the hands on a clock. This point can be inside the shape, a vertex close vertex The point at which two or more lines intersect (cross or overlap). Rotation turns a shape around a fixed point called the centre of rotation close centre of rotation A fixed point about which a shape is rotated. The result is a congruent close congruent Shapes that are the same shape and size, they are identical. is one of the four types of transformation close transformation A change in position or size, transformations include translations, reflections, rotations and enlargements.Ī rotation has a turning effect on a shape. A rotation close rotation A turning effect applied to a point or shape.
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