![]() ![]() 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. When we rotate a figure of 270 degree clockwise, each point of the given figure has to be changed from (x, y) to (-y, x) and graph the rotated figure. 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. In other words, the coordinates are the same, but the signs are. So just looking at A toĪ-prime makes me feel good that this was a 60-degree rotation. When a point rotates 180 clockwise, you will need to apply the rule (x, y) (-x, -y). And if you do that with any of the points, you would see a similar thing. Rotating 270 degrees counterclockwise about the origin is the same as reflecting over the line y x and then reflecting over the x-axis. Rotating 90 degrees clockwise is the same as rotating 270 degrees counterclockwise. Another way to thinkĪbout is that 60 degrees is 1/3 of 180 degrees, which this also looks All the rules for rotations are written so that when you're rotating counterclockwise, a full revolution is 360 degrees. 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 Let us learn the rotation formula along with a few. In general, rotation can be done in two common directions, clockwise and anti-clockwise or counter-clockwise direction. Rotation is a circular motion around the particular axis of rotation or point of rotation. The counterclockwise direction, so it's going to have a positive angle. The rotation formula is used to find the position of the point after rotation. And where does it get rotated to? Well, it gets rotated to right over here. Remember we're rotating about the origin. ![]() If this triangle is rotated 90° counterclockwise. (-y, x) Example 1 : Let F (-4, -2), G (-2, -2) and H (-3, 1) be the three vertices of a triangle. 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. When we rotate a figure of 90 degrees counterclockwise, each point of the given figure has to be changed from (x, y) to (-y, x) and graph the rotated figure. 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. Identify whether or not a shape can be mapped onto itself using rotational symmetry.- 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. ![]()
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