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May 4, 2022 · When describing a rigid motion, we will use points like P and Q, located on the geometric shape, and identify their new location on the moved geometric shape by P' and Q'. We will start with the rigid motion called a translation.
- Transformation of Translation
- Transformation of Quadratic Functions
- Transformation of Reflection
- Transformation of Rotation
- Transformation of Dilation
Translationof a 2-d shape causes sliding of that shape. To describe the position of the blue figure relative to the red figure, let’s observe the relative positions of their vertices. We need to find the positions of A′, B′, and C′ comparing its position with respect to the points A, B, and C. We find that A′, B′, and C′ are: 1. 8 units to the left...
We can apply the transformation rules to graphs of quadratic functions. This pre-image in the first function shows the function f(x) = x2. The transformation f(x) = (x+2)2shifts the parabola 2 steps right.
The type of transformation that occurs when each point in the shape is reflected over a line is called the reflection. When the points are reflected over a line, the image is at the same distance from the line as the pre-image but on the other side of the line. Every point (p,q) is reflected onto an image point (q,p). If point A is 3 units away fro...
The transformation that rotates each point in the shape at a certain number of degrees around that point is called rotation. The shape rotates counter-clockwise when the number of degrees is positive and rotates clockwise when the number of degrees is negative. The general rule of transformation of rotation about the origin is as follows. To rotate...
The transformation that causes the 2-d shape to stretch or shrink vertically or horizontally by a constant factor is called the dilation. The vertical stretch is given by the equation y = a.f(x). If a > 1, the function stretches with respect to the y-axis. If a < 1 the function shrinks with respect to the y-axis. The horizontal stretch is given by ...
A rigid motion preserves the side lengths and angle measures of a polygon. As a result, a rigid motion maintains the exact size and shape of a figure. Still, a rigid motion can affect the position and orientation of the figure.
reflections. When describing a rigid motion, we will use points like P and Q, located on the geometric shape, and identify their new location on the moved geometric shape by P' and Q'. We will start with the rigid motion called a translation. When translating an object, we move the object in a specific direction for a specific length, along a ...
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Jan 21, 2020 · Some of the basic mapping or moving of a figure in a plane are sliding, flipping, turning, enlarging, or reducing to create new figures. The four major types of transformations are: Translation (figure slides in any direction) Reflection (figure flips over a line) Rotation (figure turns about a fixed point) Dilation (figure is enlarged or reduced)
Applying a rigid motion to a geometric figure has the following effects: It doesn’t change the lengths of any line segments or sides, and doesn’t change the measure of any angles. If the figure contains lines, they remain lines after applying the rigid motion.
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Transformations and Rigid Motions of Figures. Transformations in geometry involve changing the position, size, or orientation of shapes. Rigid motions, a subset of transformations, only change the position and orientation without altering the size or shape. Examples of rigid motions include translations, rotations, and reflections.
