Question
Consider points in the plane as ordered pairs $(x, y)$ and consider the function $f$ on the plane defined by $f(x, y)=(k x+a, k y+b)$, where $k, a, b$ are real constants, and $k \neq 0$. Is $f$ a transformation? Is $f$ an isometry?
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A translation is a function of the form $T(x, y)=$ $(x-h, y-k),$ where at least one of the constants $h$ and $k$ is nonzero. (a) Show that a translation in the plane is not a linear transformation. (b) For the translation $T(x, y)=(x-2, y+1),$ determine the images of $(0,0),(2,-1),$ and (5,4) (c) Show that a translation in the plane has no fixed points.
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Determine whether the function is a linear transformation. T: R^2 → R^2, T(x, y) = (x + h, y - k), h ≠0 or k ≠0 (translation in R^2) linear transformation not a linear transformation If it is, find its standard matrix A. (If an answer does not exist, enter DNE in any cell of the matrix.)
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