![]() ![]() So what we want to do is think about, well look, if we rotate And this tool, I can put points in, or I could delete points. So positive is counter-clockwise, which is a standard convention, and this is negative, so a negative degree would be clockwise. The direction of rotationīy a positive angle is counter-clockwise. So this is the triangle PINĪnd we're gonna rotate it negative 270 degrees about the origin. We're told that triangle PIN is rotated negative 270ĭegrees about the origin. I hope this gives you more of an intuitive sense. If you want, you can connect each vertex and rotated vertex to the origin to see if the angle is indeed 90 degrees. As per the definition of rotation, the angles APA', BPB', and CPC', or the angle from a vertex to the point of rotation (where your finger is) to the transformed vertex, should be equal to 90 degrees. The rotated triangle will be called triangle A'B'C'. The point at which we do the rotation, we'll call point P. Well, let's say the shape is a triangle with vertices A, B, and C, and we want to rotate it 90 degrees. The shape is being rotated! But how do we do this for a specific angle? With your finger firmly on that point, rotate the paper on top. Now place your finger on the rotation point. Put another paper on top of it (I like to imagine this one as being something like a transparent sheet protector, and I draw on it using a dry-erase marker) and trace the point/shape. Here's something that helps me visualize it: The "formula" for a rotation depends on the direction of the rotation. I'm sorry about the confusion with my original message above. If you want to do a clockwise rotation follow these formulas: 90 = (b, -a) 180 = (-a, -b) 270 = (-b, a) 360 = (a, b). Also this is for a counterclockwise rotation. 360 degrees doesn't change since it is a full rotation or a full circle. 180 degrees and 360 degrees are also opposites of each other. So, (-b, a) is for 90 degrees and (b, -a) is for 270. Which means move three up.The way that I remember it is that 90 degrees and 270 degrees are basically the opposite of each other. And this just means take your y coordinate and add three to it, Subtract five from it, which means move five to the left. You'll sometimes see it like this, but just recognize this is just saying just take your x and Translate x units to the left or the right or three units up or down. Where they'll tell you, hey, plot the image, and How we map our coordinates, how it's able to draw the connection between the coordinates. So notice how this, I guess you could say this formula, the algebraic formula that shows Of this point is indeed negative two comma negative one. And so another way of writing this, we're going from three comma negative four to three minus five is negative two, and negative four plus So notice, well, instead ofĪn x, now I have a three. See that right over there, and we're going to add three to the y. Three and negative four, and I'm going to subtractįive from the three. ![]() If I have three comma negative four, and I want to apply this translation, what happens? Well, let me just do my coordinates. Its x coordinate is three, and its y coordinate is negative four. So at this point right over here, P has the coordinates, And so let's just test this out with this particular coordinate, And then this right over here, is saying three units up. That's what, meaning this is, this right over here, is five units to the left. So all this is saying is whatever x and y coordinates you have, this translation will make We're going to translate three units up, so y plus three. And what do we do to the y coordinate? Well, we're going to increase it by three. Me what's my coordinate in the horizontal direction Gonna take some point with the coordinates x comma y. Hopefully a pretty intuitive way to describe a translation. But you could, and this will look fancy, but, as we'll see, it's Just in plain English, by five units to the Now, there are other ways that you could describe this translation. ![]() And so the image of point P, I guess, would show up right over here, after this translation described this way. ![]() We're gonna go one, two, three, four, five units to the left, and then we're gonna go three units up. Think about other ways of describing this. So let's just do that at first, and then we're gonna Plot the image of point P under a translation by five units to the left and three units up. How to translate a point and then to actually translate that point on our coordinate plane. To do in this video is look at all of the ways of describing ![]()
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