Maths Assignment
Added on 2023-04-08
13 Pages1756 Words494 Views
MATHS ASSIGNMENT
MARCH 19, 2019
MARCH 19, 2019
A=1
B=1
C=5
D=6
E=8
F=9
Ques 1. Write down the quadrilateral Q =
i. Draw its position on a graph.
On substituting values, we get the coordinates as W (1,1), X (10,1), Y (10,10) & Z (1,9)
ii. Write down a matrix R that will rotate Q 90 degrees anti clockwise around the origin.
R =
(−1 −1 −10 −9
1 10 10 1 )
iii. Write down a matrix T that will rotate Q 90 degrees anticlockwise around the origin and increase
the size of Q by a factor 2.
T =
(−2 −2 −20 −18
2 20 20 2 )
0
1
2
3
4
5
6
7
8
9
10
11
0 1 2 3 4 5 6 7 8 9 10 11
W (1,1) X (10,1)
Y (10,10)
Z (1,9)
B=1
C=5
D=6
E=8
F=9
Ques 1. Write down the quadrilateral Q =
i. Draw its position on a graph.
On substituting values, we get the coordinates as W (1,1), X (10,1), Y (10,10) & Z (1,9)
ii. Write down a matrix R that will rotate Q 90 degrees anti clockwise around the origin.
R =
(−1 −1 −10 −9
1 10 10 1 )
iii. Write down a matrix T that will rotate Q 90 degrees anticlockwise around the origin and increase
the size of Q by a factor 2.
T =
(−2 −2 −20 −18
2 20 20 2 )
0
1
2
3
4
5
6
7
8
9
10
11
0 1 2 3 4 5 6 7 8 9 10 11
W (1,1) X (10,1)
Y (10,10)
Z (1,9)
iv. Use the transformations on Q and draw the transformed quadrilaterals RQ and TQ on the graph.
Make sure to clearly label the quadrilaterals.
R =
T =
v. Calculate the matrices R4 and T4 and explain your answers.
0
1
2
3
4
5
6
7
8
9
10
11
-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
-21 -20 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0
W’ (-1,1)
X’ (-1,10)Y’ (-10,10)
Z’ (-9,1)
W’’ (-2,2)
X’’ (-2,20)Y’’ (-20,20)
Z’’ (-18,2)
Make sure to clearly label the quadrilaterals.
R =
T =
v. Calculate the matrices R4 and T4 and explain your answers.
0
1
2
3
4
5
6
7
8
9
10
11
-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
-21 -20 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0
W’ (-1,1)
X’ (-1,10)Y’ (-10,10)
Z’ (-9,1)
W’’ (-2,2)
X’’ (-2,20)Y’’ (-20,20)
Z’’ (-18,2)
Sol.
These can not be calculated as the matrices R and T are not square matrices.
Ques 2. Graph Theory
a) The following distance table shows the distance in kilometres between some cities in the USA.
Distance
(km)
Boston Chicago Los Angeles Miami New York San
Francisco
Boston 1589 4891 2474 342 5067
Chicago 3366 2184 1352 3493
Los Angeles 4373 4539 667
Miami 2133 4990
New York 4826
i. Draw this information as a graph.
Solution:
Vertices:
City Vertex
Boston A
Chicago B
Los Angeles C
Miami D
New York E
San Francisco F
These can not be calculated as the matrices R and T are not square matrices.
Ques 2. Graph Theory
a) The following distance table shows the distance in kilometres between some cities in the USA.
Distance
(km)
Boston Chicago Los Angeles Miami New York San
Francisco
Boston 1589 4891 2474 342 5067
Chicago 3366 2184 1352 3493
Los Angeles 4373 4539 667
Miami 2133 4990
New York 4826
i. Draw this information as a graph.
Solution:
Vertices:
City Vertex
Boston A
Chicago B
Los Angeles C
Miami D
New York E
San Francisco F
End of preview
Want to access all the pages? Upload your documents or become a member.