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Question 13 Not yet answered Marked out of 10.00 Part (a) (5 MARKS Consider the following srid with integer coordinates with Oss mand 0 Sys n. How many different ways can we select a rectangle with integer coordinate corners on this gorld? For example, two different rectangles are shown, one with corners (1.1),(4,1),(4,3), (1,3) and one with corners (2.2), (2,3), (3, 3), (3,2). Justify your answer. Note that both the length and width of the rectangle can be equal but both of them must be non-zero otherwise we have a single line which is not a rectangle (Hinta rectangle is obtained from intersecting two horizontal and two vertical lines). F Flag question Part (b) (5 MARKS) Suppose we have an n-sided simple polygon and we draw all the diagonals. Assume that no three dingonals go through the same point inside the polygon. How many intersection points will we have? For example, for n = 4 there is one intersection and for n = 5 there are 5 intersections. In the figure the intersection of dingonals are highlighted with a small black circle. (Hint: each intersection point requires two diagonals). 1 A B I CA