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 from the line of reflection to the right of the line, then point A' will be 3 units away from the line of reflection to the left of the line. Thus the line of reflection acts as a perpendicular bisector between the corresponding points of the image and the pre-image. Here is the graph of a quadratic function that shows the transformation of reflection. The transformation of f(x) is g(x) = - x 3 that is the reflection of the f(x) about the x-axis. 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. In the function graph below, we observe the transformation of rotation wherein the pre-image is rotated to 180º at the center of rotation at (0,1). The transformation that is taken place here is from (x,y) → (-x, 2-y) Let us observe the rule of rotation being applied here from (x,y) to each vertex. 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.
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