And so this would be negative 90 degrees, definitely feel good about that. Lets understand the rotation of 90 degrees. A clockwise rotation of 90 is also a counterclockwise rotation of -90. And this looks like a right angle, definitely more like a rightĪngle than a 60-degree angle. Answer: To rotate the figure 90 degrees clockwise about a point, every point(x,y) will rotate to (y, -x). Clockwise rotations are also referred to as negative counterclockwise rotations. Every point makes a circle around the center: Here a triangle is rotated around. And once again, we are moving clockwise, so it's a negative rotation. The distance from the center to any point on the shape stays the same. This is where D is, and this is where D-prime is. Point and feel good that that also meets that negative 90 degrees. This looks like a right angle, so I feel good about We are going clockwise, so it's going to be a negative rotation. Too close to, I'll use black, so we're going from B toī-prime right over here. The general rule for rotation of an object 90 degrees is (x, y) -> (-y, x). Let me do a new color here, just 'cause this color is Much did I have to rotate it? I could do B to B-prime, although this might beĪ little bit too close. Now, with the interactive below, practice. The opposite of 5 is -5 and, switching the coordinates, you obtain your answer: (8, -5). Rotate the point (-5,8) around the origin 270 degrees clockwise (same as 90 degrees counterclockwise). Please save your changes before editing any questions. The rule for rotating an object 270 clockwise about the origin is to take the opposite value of the x-coordinate and then switch it with the y-coordinate. Rotate the point (7,8) around the origin 90 degrees clockwise. I can take some initial pointĪnd then look at its image and think about, well, how 90) go counterclockwise, while negative rotations (e.g. Rotate the point (5, 8) about the origin 270 clockwise. I don't have a coordinate plane here, but it's the same notion. Well, I'm gonna tackle this the same way. So once again, pause this video, and see if you can figure it out. So we are told quadrilateral A-prime, B-prime, C-prime,ĭ-prime, in red here, is the image of quadrilateralĪBCD, in blue here, under rotation about point Q. Step 1: For a 90 degree rotation around the origin, switch the x. So just looking at A toĪ-prime makes me feel good that this was a 60-degree rotation. Rotating a polygon clockwise 90 degrees around the origin. And if you do that with any of the points, you would see a similar thing.

Another way to thinkĪbout is that 60 degrees is 1/3 of 180 degrees, which this also looks

Like 2/3 of a right angle, so I'll go with 60 degrees.

One, 60 degrees wouldīe 2/3 of a right angle, while 30 degrees wouldīe 1/3 of a right angle. This 30 degrees or 60 degrees? And there's a bunch of ways The counterclockwise direction, so it's going to have a positive angle. And where does it get rotated to? Well, it gets rotated to right over here. Remember we're rotating about the origin. Hence, the transformation matrix is 2 6 3 1 Solved Example: 2 A triangle is defined by 2 4 4 2 2 4 Find the transformed coordinates after the following transformations. Points have to be rotated to go from A to A-prime, or B to B-prime, or from C to C-prime? So let's just start with A. On solving these equations we get, a 2, b 3, c 6 and d 1. So I'm just gonna think about how did each of these So like always, pause this video, see if you can figure it out. In linear algebra, a rotation matrix is a transformation matrix that is used to perform a rotation in Euclidean space.- We're told that triangle A-prime, B-prime, C-prime, so that's this red triangle over here, is the image of triangle ABC, so that's this blue triangle here, under rotation about the origin, so we're rotating about the origin here.

Rotation rules 90 geometry