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Advanced Math Project

Done By:. Advanced Math Project. Essa Essa AhMED AT1000198 Abdulla Nasser AT1000287 Ahmed Obaid AT1000272 Amer Abdulsalam AT1000268. Supervised By :. Mister. Yahya Alsakaji. Term 1 2011-201 2. Task 1. (-8,9). (9 , 9). (-8,-7). (9,-7). Task 2.

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Advanced Math Project

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  1. Done By: Advanced Math Project Essa Essa AhMEDAT1000198 Abdulla Nasser AT1000287 Ahmed ObaidAT1000272 AmerAbdulsalam AT1000268 Supervised By : Mister. YahyaAlsakaji Term 1 2011-2012

  2. Task1 (-8,9) (9 , 9) (-8,-7) (9,-7)

  3. Task2 Represent the campus (polygon) by vertex matrix. A (2,16) B(19,3) C(26,27) D(28,21) [ ] 2 19 26 28 16 3 27 21 Task 3 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. ] [ ] [ ] 4 21 28 30 2 19 26 28 2 2 2 2 = + -3 -3 -3 -3 13 0 24 18 16 3 27 21 A’ (11,6) B’(-6,6) C’(-6,-10) D’(11,-10)

  4. Task3 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? [ ] ] [ 6 57 78 84 2 19 26 28 3 = 48 9 81 63 16 3 27 21 A’ (27,27) B’(-24,27) C’(-24,-21) D’(27,-21) • c. Find the coordinates of the vertices of the original image of the campus after reflection in y=x ] [ ] [ ] [ 2 19 26 28 16 3 27 21 0 1 = 16 3 27 21 2 19 26 28 1 0 A’ (16,2) B’(3,19) C’(27,26) D’(21,28)

  5. Task 3 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. ] [ ] [ ] [ 2 19 26 28 16 3 27 21 0 1 = 16 3 27 21 -2 -19 -26 -28 -1 0 • e. Choose three vertices on the campus image that contains a land mark on the campus, use the determinant to find its area. The three vertices : (5,21) , (9,18) , (10,21) 5 21 1 area 9 18 1 1/2 = 7.5 units2 = 1/2 = (15) 10 21 1

  6. Task 4 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 + y = 10 3x + 2y = 17 Let apple be x Let bottle of orange juice be y 2 1 10 1 2 10 |c| = |x| = |y| = 3 2 17 2 3 17 = = = 2(2)-3(1) 10(2)-17(1) 2(17)-3(10) = = 4 3 = 1 = x |X|/|C| = 3/1 = 3 y = |y|/|C| = 4/1 = 4 1 apple costs 3DHS , and 1 bottle of orange juice costs 4DHS

  7. Task 5 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%. [ ] 5 3 4 2 5 3 [ ] [ ] [ ] 5 3 5 3 4 2.4 4 2 - 0.20 4 2 = 3.2 1.6 5 3 5 3 4 2.4 [ ] [ ] 5 3 4 2.4 0.80 4 2 = 3.2 1.6 5 3 4 2.4

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