1. Advanced Math Project Malik Mohammed AL Awadhi. AT1000189 Abdulla Abbas Abdulla. AT1000093 Abdulrahman Ali Albalooshi.AT1000195 Ishaq Abdulla Ishaq Abdulla. AT1000095 Done By: Supervised By : Mr. Yahya Alsakaji Term 1 2011-2012 Section: 11-13

2. Task 1 (20,2 ) (26,20) (4,11 ) (16.5,26 )

3. Task 2 Represent the campus (polygon) by vertex matrix. A (20,2)B(4,11) C(16.5,26) D(26,20) [ ] 20 4 16.5 26 2 11 26 20 Vertex matrix =

4. Use the matrix to perform the following transformations. a. The campus is moved by 2 units right and 3 units down. Find the coordinates of the new location. + = [][ ][] 20 4 16.5 26 2 11 26 20 2 2 -3 -3 22 6 18.5 28 -1 8 23 17 Task 3 ImageTranslation

5. Task 3 Use the matrix to perform the following transformations. b. Dilate the campus image so the perimeter will become 3 times more previous perimeter. What are the coordinate of the vertices of the new image? [] [] = 60 12 49.5 78 6 33 78 60 3 20 4 16.5 26 2 11 26 20

6. c. Find the coordinates of the vertices of the original image of the campus after reflection in y=x [] [] [ ] 0 1 1 0 = 20 4 16.5 26 2 11 26 20 20 4 16.5 26 2 11 26 20 Task 3

7. Use the matrix to perform the following transformations. d. Find the coordinates of the vertices of the original image of the campus after it is rotated 270° counterclockwise about the origin. [] 0 1 -1 0 [] = [ ] -20 -4 -16.5 -26 2 11 26 20 20 4 16.5 26 2 11 26 20 Task 3

8. e. Choose three vertices on the campus image that contains a land mark on the campus, use the determinant to find its area. 18.5 14.5 1 16.5 14 1 19 11 1 18.5 14.5 16.5 14 19 11 Area = ½(7.5) = 3.625 units 2 Det = 716-708.75 = 7.25 259+275.5+181.5 = 716 266+203.5+239.25 = 708.75 Task 3

9. Your campus canteen sells bottle of orange juice and apples. Ahmed bought 2 apples and 1 bottle of orange juice for 10 DHs. Abdullah bought 3 apples and 2 bottles of orange juice for 17 DHs. What is the cost of 1 apple and 1 bottle of orange juice? 2x + 1y = 10 3x + 2y = 17 10 1 17 2 = x 2 10 3 17 = y The cost of 1 apple is 3 DHs, and the cost of 1 bottle of orange juice is 4 DHs = 20-17/4-3 2 1 3 2 =3/1 = 3 2 1 3 2 = 34-30/4-3 = 4/1 = 4 Task 4

10. IAT canteen Menu Make a 3 by 2 matrix to organize these data, and then use that matrix to find the prices after discount of 20%. Chicken Sandwich Apple Orange juice 5 3 4 2 5 3 New prices = Regular Half-portion 53 4 2 5 3 - 0.2 = 4.8 2.8 3.8 1.8 4.8 2.8 Task 5

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