![]() ![]() 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. (-y,x) and (y,-x) are both the result of 90 degree rotations, just in opposite directions. 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. To see the angle of rotation, we draw lines from the center to the same point in the shape before and after the rotation. So just looking at A toĪ-prime makes me feel good that this was a 60-degree rotation. Now, if I rotate 90 degrees to the right or clockwise, I get this box in red. And if you do that with any of the points, you would see a similar thing. The points on the corners are in the chart and the calculation below is just to shade it in: 2. 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. ![]() We can think of a 60 degree turn as 1/3 of a 180 degree turn. One, 60 degrees wouldīe 2/3 of a right angle, while 30 degrees wouldīe 1/3 of a right angle. Positive rotation angles mean we turn counterclockwise. We discuss how to find the new coordinates of. Step 3 : Based on the rule given in step 1, we have to find the vertices of the reflected triangle ABC. Learn how to rotate figures about the origin 90 degrees, 180 degrees, or 270 degrees using this easier method. So the rule that we have to apply here is (x, y) -> (y, -x). Step 2 : Here triangle is rotated about 90° clock wise. This 30 degrees or 60 degrees? And there's a bunch of ways Step 1 : First we have to know the correct rule that we have to apply in this problem. 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. A rotation of 90 degrees is the same thing as -270 degrees. 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. ![]()
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