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Describe the relationship between the curves $|x| + |y| = 1$ and $|x| + |y-a| =1$, where $a>0$ is a constant.

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hint $t\mapsto t - a$ is a shift on $a$ – Norbert May 12 '12 at 13:15
Have you tried drawing them on graph paper? That might suggest something. – MJD May 12 '12 at 13:25
This might help. – Gigili May 12 '12 at 13:57

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 $a=\frac{1}{2}$.

enter image description here

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