The original position of point A relative to the origin is given by a position vector ( x, y) which we can represent using a one-by- two column matrix which we'll call matrix V. We will therefore represent our transformation using the two-by- two matrix M: The transformations we apply to a point must set values for x and y independently. Because we are dealing with a two-dimensional image, all points in the two-dimensional plane are represented by two variables ( x and y). We can therefore achieve the required transformation by multiplying y by minus one ( -1). For this to happen, x does not change, but y must be negated. The transformation involved here is one in which the coordinates of point ( x, y) will be transformed from ( x, y) to ( x, - y). Supposing we wish to find the matrix that represents the reflection of any point ( x, y) in the x-axis. A single point A with xy coordinates ( 3,4)
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