![geometry rotation examples geometry reflection rule geometry rotation examples geometry reflection rule](https://ecdn.teacherspayteachers.com/thumbitem/Transformation-Rules-for-Reflections-and-Rotations-1546503-1500873468/original-1546503-1.jpg)
So just looking at A toĪ-prime makes me feel good that this was a 60-degree rotation. 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. 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. Our Educational Directors can create a tutoring plan that works with even the busiest schedules, so reach out today.- 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. Less confident students can get all the help they need as they catch up with their peers and regain confidence in their skills. Working alongside a tutor can help advanced students challenge themselves with new, interesting topics that their teacher doesn't have time to cover. When you reach out to Varsity Tutors to pair your student with a tutor, you get access to a math professional who has been carefully vetted and interviewed. Scale Factor Flashcards covering the ReflectionsĬollege Algebra Flashcards Practice tests covering the ReflectionsĬollege Algebra Diagnostic Tests Get your student started with a math tutor
![geometry rotation examples geometry reflection rule geometry rotation examples geometry reflection rule](https://i.ytimg.com/vi/zhATKh7ikG4/hqdefault.jpg)
In other words, ( x, y ) becomes ( y, x ) The rule is simple: We flip the two values. The rule in this case is ( x, y ) becomes ( - x, y ).īut what about a reflection over a diagonal line? In other words, what if y = x? Take a look: We can see that a coordinate on the reflected image has become negative, but this time it's the x value instead of the y value. Now let's see what happens when we reflect a point over the y-axis: In other words: ( x, y ) becomes ( x, - y ) with a reflection over the x-axis. This is because when we reflect an image over the x-axis, we're always left with a negative y-value. You might have also spotted the fact that the reflective image now has a negative coordinate point. If we have just one point to work with, reflections are simple:Īs you can see, this point has been reflected over the x-axis. We call this fixed line the "line of reflection." When we reflect figures, we must map every one of their points across a fixed line. But if the object is not symmetrical, it changes when we reflect it.īecause only the position changes, reflected images are "congruent" or equal to their original images. This is the same concept as flipping a card upside down. When we reflect a figure, we flip it across some mirror line. You might recall that when we transform a geometric shape, we simply change its shape and or position on a plane.Ī reflection does not affect the size of the original shape, and it only affects its position.
![geometry rotation examples geometry reflection rule geometry rotation examples geometry reflection rule](https://useruploads.socratic.org/R5cUlRDERjqn0bgq7V0g_reflection%20y%20axis.jpg)
What is a reflection?Ī reflection is a type of transformation. But what does the term "reflection" mean in the world of math? While the general concept is the same, we need to cover some specific rules that apply only to geometrical reflection. After all, we see our own reflections whenever we look in the mirror.