Describing transformation and its different types
If I have some triangle that looks like this. Example shows multiple transformations applied to an object to create a xylophone bar. Well to go from this point to this point, we could rotate around this point. So if you're transforming some type of a shape. The scaling process is shown in the following figure.
In this way, we can represent the point by 3 numbers instead of 2 numbers, which is called Homogenous Coordinate system. Similar to the rotation transformations, scaling transformations are applied at a pivot point. Example shows the code for the rotation transformation. Otherwise, the image might appear where it is not intended to be. If the shape in question has been rotated, reflected or translated, it will remain the same size. Example shows the code for the scale transformation. Now let's think about whether our transformation could be a reflection. Moreover, every point on the object makes a circular movement around the centre point. Well let's just imagine that we take these sides and we stretch them out so that we now have A is over here or A prime I should say is over there. And my segment lengths are for sure going to be different now. And so let's think about this a little bit. They say a sequence of transformations is described below.
Measure from the point to the mirror line, 2. Your scale factor is -2, so you must multiply the distance between the centre point of enlargement and each of your co-ordinates by -2 respectively.
Well a reflection is also a rigid transformation and so we will continue to preserve angle measure and segment lengths. This will display your understanding of transformations to the examiner who is marking your paper and earn you maximum method marks. The initial position of the xylophone bar is defined by x, y, and z coordinates.
That's a rigid transformation, it would preserve both segment lengths and angle measures. If you were to rotate around to this point right over here, this point would map to that point, and that point would map to that point. But angles are going to continue to be preserved.
And so pause this video again and see if you can figure out whether measures, segment lengths, both or neither are going to be preserved. Symmetry Video transcript - [Instructor] In past videos, we've thought about whether segment lengths or angle measures are preserved with a transformation.
For more information, see the API documentation. Example a - Describe the rotation which has occurred to the red triangle in the following diagram: Solution a - When rotating an object, the distance between the centre and any point on the object must stay the same. Angles preserved. Example shows the code for the rotation transformation. So in this situation, everything is going to be preserved. If you were to rotate around to this point right over here, this point would map to that point, and that point would map to that point. Example a - Write the displacement vector which describes triangle P's translation to triangle Q: Solution a - By counting the squares in the grid or by counting the numbers on the axes, you can see that, in order to be translated to triangle Q, triangle P has moved 1 place downwards and 4 places to the right. Let's say that B prime is now over here. Your new image should look like this: During your GCSE maths exam, you may also be required to resize various objects. But if you throw a stretch in there, then all bets are off. Shearing is also termed as Skewing. Angle measure and segment lengths. Carefully calculate values when specifying the pivot point. We are going from 4, negative 1 to 7, negative 3.
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