![]() Transformations, and there are rules that transformations follow in coordinate geometry. In summary, a geometric transformation is how a shape moves on a plane or grid. If you have an isosceles triangle preimage with legs of 9 feet, and you apply a scale factor of 2 3 \frac 3 2 , the image will have legs of 6 feet. Mathematically, a shear looks like this, where m is the shear factor you wish to apply:ĭilating a polygon means repeating the original angles of a polygon and multiplying or dividing every side by a scale factor. Italic letters on a computer are examples of shear. Shearing a figure means fixing one line of the polygon and moving all the other points and lines in a particular direction, in proportion to their distance from the given, fixed-line. The clockwise rotation usually is indicated by the negative sign on magnitude. The most common rotations are usually 90, 180 and 270. You can find both the Clockwise and AntiClockwise directions of rotation by the rotation calculator. ![]() If the figure has a vertex at (-5, 4) and you are using the y-axis as the line of reflection, then the reflected vertex will be at (5, 4). We need to understand that the rotation can be done in both Clockwise and AntiClockwise directions. Reflecting a polygon across a line of reflection means counting the distance of each vertex to the line, then counting that same distance away from the line in the other direction. To rotate 270°: (x, y)→ (y, −x) (multiply the x-value times -1 and switch the x- and y-values) To rotate 180°: (x, y)→(−x, −y) make(multiply both the y-value and x-value times -1) To rotate 90°: (x, y)→(−y, x) (multiply the y-value times -1 and switch the x- and y-values) Rotation using the coordinate grid is similarly easy using the x-axis and y-axis:
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