Each of the four inequalities given below defines a region in the  plane. One of these four regions does not have the following property. For any two points  and  in the region, the point  is also in the region. The inequality defining this region is a) b) c) d)

Question ID - 55871 | SaraNextGen Top Answer Each of the four inequalities given below defines a region in the  plane. One of these four regions does not have the following property. For any two points  and  in the region, the point  is also in the region. The inequality defining this region is a) b) c) d)

Answer Key / Explanation : (c) -

(c)

represents interior region of circle, where on taking any two points the midpoint of that segment will also lie inside that circle

and

Which represents the interior region of a square with its sides  and  in which for any two points, their midpoint also lies inside the region

represents the exterior region of hyperbola in which we take two points (4, 3) and . Then their midpoint (4, 0) does not lie in the same region (as shown in the figure)

represents interior region of parabola in which for any two points, their midpoint also lies inside the region