d in the plane with no three collinear – Discussion Forum

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Virat

Asked: October 3, 2026In: Class 9 Maths

Consider 4 points A, B, C, D in the plane with no three collinear. Answer the following questions. Some answers may require you to consider different cases, depending on how the points are positioned in the plane. (i) How many different quadrilaterals do they form if the quadrilateral is allowed to be self-intersecting or non-convex? (ii) How many of these quadrilaterals are self-intersecting? How many are convex?

(i) Exactly 3 distinct cyclic edge orderings can be formed. (ii) If the 4 points form a convex hull: 1 is convex and 2 are self-intersecting. If 1 point is inside: 0 are convex, 3 are non-convex and 0 self-intersect. Class ...