Advanced Math Project

Mayed Hassan AT1000443 Mohammad Ahmed AT1000324Salem Adel AT1000336Ali Bin Haidr AT1000385

Done By:

Supervised By :Mr. Yahya

Term 12011-2012

Task 1

(15, 11)

(7,9) (9,-7)

(-8,-1)

Task 2 Represent the campus (polygon) by vertex matrix.

A (8,1) B(16,4) C(15,11) D(7,9)

[ ]8 16 15 71 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.[ ]8 16 15

71 4 11 9

+[ ]2 2 2 2-3 -3 -3 -3

=[ ]10 18 17 9 -2 1 8

6A’ (10,-2) B’(18,1) C’(17,8)D’(9,6)

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?

[ ]8 16 15 71 4 11 9

=[ ]24 48 45 21 3 12 33 27

A’ (24,3) B’(48,12) C’(45,33) D’(21,27)

3

c. Find the coordinates of the vertices of the original image of the campus after reflection in y=x

[ ]0 11 0

[ ]=[ ]A’ (1,8) B’(4,16) C’(11,15)D’(9,7)

8 16 15 71 4 11 9

8 16 15 7

1 4 11 9

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.

[ ]0 1-1 0

[ ]=[ ]The three vertices : (7,9) , () , (7,-5 )

8 16 15 71 4 11 9

-8 -16 -15 -7

1 4 11 9

e. Choose three vertices on the campus image that contains a land mark on the campus, use the determinant to find its area.

8 1 1 16 4 1 15 11 1

area= =1/2 1/2(59) = 29.5 units2

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?

Apple = xBottle of orange = y

2x + y = 103x + 2y = 17

2 1 3 2=|c| 10 1

17 2=|x| 2 10 3 17

=|y|

= = =2(2)-3(1) 2(17)-3(10)

10(2)-17(1)= = =1 43

=x =y|X|/|C| = 3/1 = 3

|y|/|C| = 4/1 = 41 apple costs 3Dhs , and 1 bottle of orange juice costs 4Dhs

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

25 3[ ]5 3 4

25 3

- 0.20[ ]5 3 4

25 3

= [ ]4 2.4 3.2 1.64 2.4 [ ]5

3 4 25 3

0.80 = [ ]4 2.4 3.2 1.64 2.4

Regular

Half-Portion

Chicken sandwich

5 3

Apple 4 2Orange Juice 5 3