This document summarizes an advanced math project done by three students. It contains five tasks: 1) Plotting points on a graph; 2) Representing a campus as a vertex matrix; 3) Performing transformations on the campus matrix like translation, dilation, reflection, and rotation; 4) Solving a system of equations to find prices of apples and orange juice; 5) Organizing menu prices in a matrix and applying a 20% discount.

1. Advanced Math Project
Done By:
Meshal Mohammed AT1000443
Sultan Khalid AT1000324
Ali Ganim AT1000385
Supervised By :
Miss. Lakshmi Krishnan
Term 1
2011-2012

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

3. Task 2
Represent the campus (polygon) by vertex matrix.
A (9,9) B(-8,9) C(-8,-7) D(9,-7)
[ 9
9
-8
9
-8
-7
9
-7 ]
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.
[ 9
9
-8
9
-8
-7
9
-7 ][ +
2
-3
3
2
-3
2
-3
2
] [
-
=
6
11
11
-6
6
-6
-10 ]
-10
A’ (11,6) B’(-6,6) C’(-6,-10) D’(11,-10)

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?
3 [ 9
9
-8
9
-8
-7
9
-7 ][ =
27
27
21
-24
27 -21
-24 27
- ]
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
[ ][ 0
1
1
0
9
9
-8
9
-8
-7
9
-7 ][=
9
9
9
-8
-7
-8 9]
-7
A’ (9,9) B’(9,-8) C’(-7,8) D’(-7,9)

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.
[ ][ 0
1
-1 0
9
9
-8
9
-8
-7
9
-7 ][=
9
-9
9
8
-7
8 ]
-7
-9
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 : (2,9) , (-1,-6) , (7,-5 )
2 9
1
area = 1/2 -1 -6 = 1/2 (117) = 58 units2
1
7 -5
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?
Let apple be x 2x + y = 10
Let bottle of orange juice be y 3x + 2y = 17
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)
= 1 = 3 = 4
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
5
3
2
[ ] [ ][ ]
5
3
4
5
3
2 - 0.20
5
3
4
5
3
2 =
4
3.2
4
2.4
1.6
2.4
[ ][ ] 0.80
5
3
4
5
3
2 =
4
3.2
4
2.4
1.6
2.4