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Advanced Math Project

Done By:. Advanced Math Project. Term 1 2011-2012. Mayed Hassan AT1000443 Mohammad Ahmed AT1000324 Salem Adel AT1000336 Ali Bin Haidr AT1000385. Supervised By :. Mr. Yahya. Task 1. (15, 11). ( 7 ,9). (9,-7). (-8,-1). Task 2 .

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Advanced Math Project

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  1. Done By: Advanced Math Project Term 1 2011-2012 Mayed Hassan AT1000443 Mohammad Ahmed AT1000324 Salem Adel AT1000336 Ali Bin Haidr AT1000385 Supervised By : Mr. Yahya

  2. Task 1 (15, 11) (7,9) (9,-7) (-8,-1)

  3. Task2 Represent the campus (polygon) by vertex matrix. A (8,1) B(16,4) C(15,11) D(7,9) [ ] 8 16 15 7 1 4 11 9 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. ] [ ] [ ] 10 18 17 9 8 16 15 7 2 2 2 2 = + -2 1 8 6 -3 -3 -3 -3 1 4 11 9 A’ (10,-2) B’(18,1) C’(17,8) D’(9,6)

  4. 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? [ ] ] [ 24 48 45 21 8 16 15 7 3 = 3 12 33 27 1 4 11 9 A’ (24,3) B’(48,12) C’(45,33) D’(21,27) • c. Find the coordinates of the vertices of the original image of the campus after reflection in y=x ] [ ] [ ] [ 8 16 15 7 14 11 9 0 1 = 1 4 11 9 8 16 15 7 1 0 A’ (1,8) B’(4,16) C’(11,15) D’(9,7)

  5. Task3 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. ] [ ] [ ] [ 8 16 15 7 1 4 11 9 0 1 = 14 11 9 -8 -16 -15 -7 -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 : (7,9) , () , (7,-5 ) 81 1 area 16 4 1 1/2 = 29.5 units2 = 1/2 = (59) 15 11 1

  6. Task 4 Your campus cafeteria 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 Apple = x Bottle of orange = 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 = y = x |X|/|C| = 3/1 = 3 |y|/|C| = 4/1 = 4 1 apple costs 3Dhs , and 1 bottle of orange juice costs 4Dhs

  7. Task 5 IAT Cafeteria 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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