a) Suppose Graham's scan executes n points, where n >= 3. Prove that, at the end of the S consists of, from bottom to top, exactly the vertices of convex hull in counter-clockwise order. program, the

Question 5: Consider the following graph. Find the shortest path from 'a' to all other vertices using Dijkstra's algorithm. Draw graph diagrams to show all intermediate steps. (. 1 4 3 4 a i 3 с 1 2 d 80 g 3

Perform scaling on a triangle (1, 1), (8, 1) and (1, 9) with a scaling factor of 2 in both x y-directions. Find the final coordinates and of the triangle.

If n points are connected to fom a closed polygon as shown below, the area of the polygon can be compuled as n-2 Area = (%)E (*»1 + x ) (y»1 - y ) =0 Notice that although the ilustrated polygon has only 6 distinct comers, n for his polygon is 7 because the algorithmexpects that the last point (x.ya) will be repeat of the initial point, (Ko.yo). Define a structure for a point. Each point contains x coordinate and y coordinate. The represe ntation of a Polygon must be an array of structures in your program. Write a C program that takes the number of actual points (n-1) from the user. After that, user enters x and y coordinates of each point. (The last point will be repeat of the initial point). Writo a compute Are a function which returns the area of the Polygon. Print he area of the Polygon in main. Display the area with wo digts after the decimal point. Note: The absolute value can be computed with fabs function. Example: double x.50: fabs(x) is 5.0 double x 0.0: fabs(x) is 0.0 double…