It's talking about taking a set of coordinates or a set of points, and then changing them into a different set of coordinates or a different set of points. For example, this right over here, this is a quadrilateral we've plotted it on the coordinate plane.
This is a set of points, not just the four points that represent the vertices of the quadrilateral, but all the points along the sides too. There's a bunch of points along this. You could argue there's an infinite, or there are an infinite number of points along this quadrilateral. This right over here, the point X equals 0, y equals negative four, this is a point on the quadrilateral.
Now, we can apply a transformation to this, and the first one I'm going to show you is a translation, which just means moving all the points in the same direction, and the same amount in that same direction, and I'm using the Khan Academy translation widget to do it. Let's translate, let's translate this, and I can do it by grabbing onto one of the vertices, and notice I've now shifted it to the right by two. Every point here, not just the orange points has shifted to the right by two.
This one has shifted to the right by two, this point right over here has shifted to the right by two, every point has shifted in the same direction by the same amount, that's what a translation is.
Now, I've shifted, let's see 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. That is a translation, but you could imagine a translation is not the only kind of transformation. In fact, there is an unlimited variation, there's an unlimited number different transformations. So, for example, I could do a rotation. So for example, I could 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, actually let me see.
So if I start like this I could rotate it 90 degrees, I could rotate 90 degrees, so I could rotate it, I could rotate it like, that looks pretty close to a degree rotation. So, every point that was on the original or in the original set of points I've now shifted it relative to that point that I'm rotating around.
I've now rotated it 90 degrees, so this point has now mapped to this point over here. This point has now mapped to this point over here, and I'm just picking the vertices because those are a little bit easier to think about.
Geometry Perpendicular and parallel Overview Angles, parallel lines and transversals. Geometry Similarity Overview Polygons Triangles. Geometry Right triangles and trigonometry Overview Mean and geometry The converse of the Pythagorean theorem and special triangles.
Geometry Quadrilaterals Overview Angles Properties of parallelograms. Non-Rigid Transformations A non-rigid transformation can change the size or shape, or both size and shape, of the preimage. Transformation Examples There are five different types of transformations, and the transformation of shapes can be combined.
Here are a preimage and an image. What two transformations were carried out on it? The preimage has been rotated and dilated shrunk to make the image. Transformations in the Coordinate Plane On a coordinate grid, you can use the x-axis and y-axis to measure every move.
Next Lesson: Rotational Symmetry. Instructor: Malcolm M. Malcolm has a Master's Degree in education and holds four teaching certificates. He has been a public school teacher for 27 years, including 15 years as a mathematics teacher. Local and online. View Tutors. Geometry Help. Tutors online. Ask a question Get Help. View Math Tutors. Popular cities for math tutoring Math Tutors New York. Find a math tutor near you Learn faster with a math tutor. Find a tutor locally or online.
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