Describe the relationship between the curves $|x| + |y| = 1$ and $|x| + |y-a| =1$, where $a>0$ is a constant.
Relationship between two absolute value curves
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algebra-precalculus
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0[This](http://www.wolframalpha.com/input/?i=plot%20%7Cx%7C%2B%7Cy%7C%3D1%20%26%26%20%7Cx%7C%2B%7Cy-1%7C%3D1&t=crmtb01) might help. – 2012-05-12
1 Answers
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For every point $(x,y)$, satisfying $|x|+|y|=1$, the point $(x_1, y_1) = (x, y+a)$ will satisfy $|x_1| + |y_1-a| = 1$.
Now describe the transformation $(x,y) \mapsto (x, y+a)$. In the picture above $a=\frac{1}{2}$.