![]() ![]() 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. 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. 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. So, I had quadrilateral BCDE, I applied a 90-degree counterclockwise rotation around the point D, and so this new set of 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. Two, three, four, five, this not-irregular If we reflect, we reflect acrossĪ line, so let me do that. To reflect it, let me actually, let me actually make a line like this. This distance from the line, and this point over here This, its corresponding point in the image is on the other side of the Original shape they should be mirror images across Reflect across something? One way I imagine is if this was, we're going to get its mirror image, and you imagine thisĪs the line of symmetry that the image and the I could reflect it acrossĪ whole series of lines. Return to more free geometry help or visit t he Grade A homepage.That I've just showed you, the translation, the Is the same distance but on the other side. Return to the top of basic transformation geometry. This is typically known as skewing or distorting the image. In a non-rigid transformation, the shape and size of the image are altered. You just learned about three rigid transformations: This type of transformation is often called coordinate geometry because of its connection back to the coordinate plane. Rotation 180° around the origin: T( x, y) = (- x, - y) In the example above, for a 180° rotation, the formula is: ![]() Some geometry lessons will connect back to algebra by describing the formula causing the translation. That's what makes the rotation a rotation of 90°. Also all the colored lines form 90° angles. Notice that all of the colored lines are the same distance from the center or rotation than than are from the point. The figure shown at the right is a rotation of 90° rotated around the center of rotation. Also, rotations are done counterclockwise! You can rotate your object at any degree measure, but 90° and 180° are two of the most common. Reflection over line y = x: T( x, y) = ( y, x)Ī rotation is a transformation that is performed by "spinning" the object around a fixed point known as the center of rotation. ![]() Reflection over y-axis: T(x, y) = (- x, y) Reflection over x-axis: T( x, y) = ( x, - y) In other words, the line of reflection is directly in the middle of both points.Įxamples of transformation geometry in the coordinate plane. The line of reflection is equidistant from both red points, blue points, and green points. Notice the colored vertices for each of the triangles. Let's look at two very common reflections: a horizontal reflection and a vertical reflection. The transformation for this example would be T( x, y) = ( x+5, y+3).Ī reflection is a "flip" of an object over a line. More advanced transformation geometry is done on the coordinate plane. In this case, the rule is "5 to the right and 3 up." You can also translate a pre-image to the left, down, or any combination of two of the four directions. The formal definition of a translation is "every point of the pre-image is moved the same distance in the same direction to form the image." Take a look at the picture below for some clarification.Įach translation follows a rule. The most basic transformation is the translation. Translations - Each Point is Moved the Same Way ![]() The original figure is called the pre-image the new (copied) picture is called the image of the transformation.Ī rigid transformation is one in which the pre-image and the image both have the exact same size and shape. ![]()
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