Each of the four inequalities given below defines a region in the \( x y \) plane. One of these ...

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Each of the four inequalities given below defines a region in the \( x y \) plane. One of these four regions does not have the following property. For any two points \( \left(x_{1}, y_{1}\right) \) and \( \left(x_{2}, y_{2}\right) \) in the region, the point \( \left(\left(x_{1}+x_{2}\right) / 2,\left(y_{1}+y_{2}\right) / 2\right) \) is also in the region. The inequality defining this region is
(a) \( x^{2}+2 y^{2} \leq 1 \)
(b) \( \max \{|x|,|y|\} \leq 1 \)
(c) \( x^{2}-2 y^{2} \leq 1 \)
(d) \( y^{2}-x \leq 0 \)
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