And so this would be negative 90 degrees, definitely feel good about that. And this looks like a right angle, definitely more like a rightĪngle than a 60-degree angle. And once again, we are moving clockwise, so it's a negative rotation. 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.

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. I can take some initial pointĪnd then look at its image and think about, well, how 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. So just looking at A toĪ-prime makes me feel good that this was a 60-degree rotation. The transformation for this example would be T(x, y) (x+5, y+3). More advanced transformation geometry is done on the coordinate plane. And if you do that with any of the points, you would see a similar thing. In this case, the rule is '5 to the right and 3 up.' You can also translate a pre-image to the left, down, or any combination of two of the four directions. 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. 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. 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. 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.

Rules for rotations in geometry