![]() ![]() 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 Introduce you to in this video is the notion of a Regardless of whether you find algebraic representation easier or more efficient than using a graph, I hope that this helps you and gives you a clearer understanding of translating, rotating, and reflecting. You can also use this key when reflecting points or shapes across the x-axis or y-axis.Įxample: If you wanted to reflect (5, 3) over the y-axis, you would end up with (-5, 3) based on the key. ![]() Reflection: Over the X-Axis -> ( x, -y) & Over the Y-Axis -> (*-x, y*) If you follow the key, the point would become (5, -2). If you do not want to use a graph, using the key above can help you rotate points and shapes in a clockwise direction.Įxample: Say there is a point (2, 5) and you wanted to rotate the point 90 degrees clockwise. Rotation: 90 degrees clockwise -> ( y, -x), 180 degrees clockwise -> (*-x, -y*), 270 degrees clockwise -> (*-y, x*) If you wanted to translate an entire shape without using a graph, you would do this method with all of the necessary points of the shape. You would eventually end up with the translated point as (3, 3). In this scenario, you would add 1 and 2 to each of the point's coordinates making it look something like this: (1 + 2, 2 + 1). You can translate points and shapes in any direction using this key by adding or subtracting the distance moved.Įxample: Pretend that there is a point like (1, 2) and you want to move the point up 1 and to the right 2. Translation: Right/Up -> ( x + n, y + n) & Left/Down -> ( x - n, y - n) For the sake of this video, Sal used a graph to translate, rotate, and reflect the quadrilateral. There is another way-*algebraic representation. Sorry if this isn't a question, and I hope it helps! :) Because I think that this information is valuable for the KA community, I also decided to post my answer here. Hi! Someone down in the thread asked about other ways of translating, rotating, and reflecting points, and I answered their question. ![]()
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