translation rules in geometry 180 degree rotation

TRANSLATION RULES IN GEOMETRY 180 DEGREE ROTATION FULL

You imagine the reflection of an image in a mirror or on the water, and that's exactly what Notion of a reflection, and you know what reflection Now let's look at another transformation, and that would be the That are on our quadrilateral, I could rotate around, I could I don't have to just, let me undo this, I don't have to rotateĪround just one of the points that are on the original set Points this is the image of our original quadrilateralĪfter the transformation. So, I had quadrilateral BCDE, I applied a 90-degree counterclockwise rotation around the point D, and so this new set of The point of rotation, actually, since D is actually the point of rotation that one actually has not shifted, and just 'til you get some terminology, the set of points after youĪpply the transformation this is called the image Vertices because those are a little bit easier to think about. To this point over here, and I'm just picking the I've now rotated it 90 degrees, so this point has now mapped Points I've now shifted it relative to that point So, every point that was on the original or in the original set of

So I could rotate it, I could rotate it like, that looks pretty close to a 90-degree rotation. So if I start like this IĬould rotate it 90 degrees, I could rotate 90 degrees, Rotate it around the point D, so this is what I started with, if I, let me see if I can do this, I could rotate it like,Īctually let me see. I have another set of points here that's represented by quadrilateral, I guess we could call it CD orīCDE, and I could rotate it, and I rotate it I would In fact, there is an unlimited variation, there's an unlimited numberĭifferent transformations. That is a translation,īut you could imagine a translation is not the If I put it here every point has shifted to the right one and up one, they've all shifted by the same amount in the same directions. In the same direction by the same amount, that's Shifted to the right by two, every point has shifted This one has shifted to the right by two, this point right over here has Just the orange points has shifted to the right by two. Onto one of the vertices, and notice I've now shifted Let's translate, let's translate this, and I can do it by grabbing That same direction, and I'm using the Khan Academy To show you is a translation, which just means moving all the points in the same direction, and the same amount in Transformation to this, and the first one I'm going This right over here, the point X equals 0, y equals negative four, this is a point on the quadrilateral.

You could argue there's an infinite, or there are an infinite number of points along this quadrilateral. Of the quadrilateral, but all the points along the sides too. Not just the four points that represent the vertices For example, this right over here, this is a quadrilateral we've plotted it on the coordinate plane.

It's talking about taking a set of coordinates or a set of points, and then changing themĭifferent set of points. You're taking something mathematical and you're changing it into something else mathematical, In a mathematical context? Well, it could mean that Something is changing, it's transforming from Transformation in mathematics, and you're probably used to Gets us to point A.Introduce you to in this video is the notion of a That and it looks like it is getting us right to point A. Our center of rotation, this is our point P, and we're rotating by negative 90 degrees. Which point is the image of P? So once again, pause this video and try to think about it. Than 60 degree rotation, so I won't go with that one. And it looks like it's the same distance from the origin. Like 1/3 of 180 degrees, 60 degrees, it gets us to point C.

TRANSLATION RULES IN GEOMETRY 180 DEGREE ROTATION FULL

So does this look like 1/3 of 180 degrees? Remember, 180 degrees wouldīe almost a full line. One way to think about 60 degrees, is that that's 1/3 of 180 degrees. So this looks like aboutĦ0 degrees right over here. P is right over here and we're rotating by positive 60 degrees, so that means we go counterĬlockwise by 60 degrees. It's being rotated around the origin (0,0) by 60 degrees. Which point is the image of P? Pause this video and see That point P was rotated about the origin (0,0) by 60 degrees. I included some other materials so you can also check it out. There are many different explains, but above is what I searched for and I believe should be the answer to your question. There is also a system where positive degree is clockwise and negative degree anti-clockwise, but it isn't widely used. Product of unit vector in X direction with that in the Y direction has to be the unit vector in the Z direction (coming towards us from the origin). Clockwise for negative degree.įor your second question, it is mainly a conventional that mathematicians determined a long time ago for easier calculation in various aspects such as vectors.

Translation rules in geometry 180 degree rotation