![]() Transformations, and there are rules that transformations follow in coordinate geometry. When an object is reflected across a line (or plane) of reflection, the size and shape of the object does not change, only its configuration the objects are therefore congruent before and after the transformation. In summary, a geometric transformation is how a shape moves on a plane or grid. In geometry, a reflection is a rigid transformation in which an object is mirrored across a line or plane. 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. 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). 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: The other two points to remember in a translation are-( − 7, − 1 ) → ( − 7 + 9, − 1 + 5 ) → ( 2, 4 ) (-7,-1)\to (-7+9,-1+5)\to (2,4) ( − 7, − 1 ) → ( − 7 + 9, − 1 + 5 ) → ( 2, 4 )ĭo the same mathematics for each vertex and then connect the new points in Quadrants II and IV. The rigid transformation has vast uses in geometry. What is a transformation in math The transformation definition in math is that a transformation is a manipulation of a geometric shape or formula that maps the shape or formula from its preimage. We did this with a point, but the same logic is applicable when you have a line or any kind of figure. Transformations Three of the most important transformations are: After any of those transformations (turn, flip or slide), the shape still has the same size, area, angles and line lengths. The third move is rotation, where the object is rotated from a fixed pivot point, called the rotocenter. We will then move the point 3 units UP on the y-axis, as the translation number is (+3). So, we will move the point LEFT by 1 unit on the x-axis, as translation number is (-1). We are given a point A, and its position on the coordinate is (2, 5). ![]() Use the same logic for y-axis if the translation number is positive, move it up, and if the translation number is negative, move the point down. On our x-axis, if the translation number is positive, move that point right by the given number of units, and if the translation number is negative, move that point to its left. ![]() The key to understanding translations is that we are SLIDING a point or vertices of a figure LEFT or RIGHT along the x-axis and UP or DOWN along the y-axis. ![]()
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