please write code in java.
Observe the following rules DO NOT use System exito DO NOT add the project or package statements DO NOT change the class name. DO NOT change the headers of ANY of the given methods DO NOT add any new class fields ONLY display the result as specified by the example for each problem DO NOT print other messages, follow the examples for each problem USE Sidin, Sidout SidRandom and Sid Draw libraries Polygon transform (25 points) Write a library of Static methods that performs various geometric transforms on polygons Mathematically, a polygon is defined by its sequence of vertices Yol X1) X 2.) In Java, we will represent a polygon by storing the -and y coordinates of the vertices in two parallel arrays and y . Here to the lyrics 02). double (11) double Y. 2.1 Three useful geometric transforms are scale, translate and rotate Scale the coordinates of each vertex (x,y) by a factor a Xi-axi yira y Translate each vertex (x, y) by a given offset (dx, dy) x1 = x + dx Vi= y + dy Rotate each vertex (x, y) by e degrees counterclockwise, around the origin X; = x;cos e- y sin e Y;= y, cos @ + x, sin e Write a two-dimensional transformation library by implementing the following API public class Polygon Transform // Returns a new array object that is an exact copy of the given array: // The given array is not mutated. public static double1 copy(double[] array) 1/ Scales the polygon by the factor alpha public static void scaledouble[] , double y, double alpha) 7 Translates the polygon by (dx, dy public static void translate(doublecl *. doublefly, double dx, double dy) W Rotates the polygon theta degrees counterlaced about the origins public static void rotate(double] , double() y, double theta) 17 Tests each of the APT methods by directly calling them public static void main(String args) Note that the transformation methods scale), translate() and rotate() mutate the polygons. Here are some example test cases (tests for copy) are not shown) 1/ Scales polygon by the factor 2 straw.setScale(-5.0, 5.0); double) * - , 1, 1, 0) poublely - (0, 0, 2, 1); souble alpha - 2.0 Store.setPencolor (St Draw,RED): Strapolygon. ) scale(x, Y. alpha) straw.setPenColor(5tdraw.BLUE); straw.polygon (x, y): // Translates polygon by (2.1). Straw.setScale(-5.0, 5.0) doublell X - [ 0, 1, 1); doublefly - {0, 0, 2, 1); double dx - 2.0, dy - 1.0 stobrau.setPen Color (Str.RO): Straw.polygon(x, y): translate(x, y, dx dy): Storiw.setPencolor (Stora. U Str.polygon. ) 11 Rotates polygon 45 degrees stran.setScale(-5.0, 5.0); Houble] - (1. 1. ) Joublecl y .(0, , 2, 1): Jouble theta - 45.0 KtDraw, setpencolor (Straw.RED): Straw.polygon, Y): rotate(x, y, theta); Story.setPencolor (Straw. BLUE) Straw.polygon. Y): 10.0 100 100
