Question

Two distinct lines, l₁ and l₂ , intersect at a point P. In addition to P, four distinct points are marked out on l₁ and three distinct points on l₂ . A mathematician decides to join some 6a. [2 marks] Find how many sets of four points can be selected which can form the vertices of a of these eight points to form polygons. quadrilateral.

Answer 1

To form a quadrilateral using the given points, we need to select 4 points out of the total 8 points. There are 70 different sets of four points that can be selected to form a quadrilateral.

Step-by-step explanation:

To form a quadrilateral using the given points, we need to select 4 points out of the total 8 points. In combinatorial mathematics, this is known as selecting 4 objects from a set of 8 objects, which can be represented by the notation 8C4. The formula for combinations is nCr = n! / (r!(n-r)!), where n is the total number of objects and r is the number of objects to be selected. Plugging in the values, we have 8C4 = 8! / (4!(8-4)!) = 70. Therefore, there are 70 different sets of four points that can be selected to form a quadrilateral