Filter
Top Products
EL-9900 Graphing Calculator
Linear Transformation
Use the matrix to find four types of the linear transformation of x-axis symmetric
transformation, y-axis symmetric transformation, similar transformation and
revolution around the origin.
Calculation
FLOWCHART
PROGRAMME LIST
Array declaration
Entry of coordinates (X,Y)
Start
End
Entry of type
To label XSYMMETRY
Declare array size, etc.
matH(2,2), matD(2,1), matA(2,1)
Enter coordinates before transformation.
Type of transformation specified
with no from 1 to 4.
Jumps to destination corresponding
to entered number.
XSYMMETRY
Data set of x-axis symmetric transformation
matH(1,1) = 1, matH(1,2) = 0,
matH(2,1) = 0, matH(2,2) = -1
YSYMMETRY
Data set of y-axis symmetric transformation
matH(1,1) = -1, matH(1,2) = 0,
matH(2,1) = 0, matH(2,2) = 1
{2, 2} dim(mat H)
{2, 1} dim(mat D)
{2, 1} dim(mat A)
Print "Input POINT
Input X
Input Y
X mat D(1, 1)
Y mat D(2, 1)
Label TYPE
Print "SELECT 1, 2, 3, 4
Input S
ClrT
If S=1 Goto XSYMMETRY
If S=2 Goto YSYMMETRY
If S=3 Goto SIMRATIO
If S=4 Goto ROTATE
GotoTYPE
Label XSYMMETRY
1 mat H(1, 1)
0 mat H(2, 1)
0 mat H(1, 2)
-1 mat H(2, 2)
Goto TRANS
Label YSYMMETRY
-1 mat H(1, 1)
0 mat H(2, 1)
0 mat H(1, 2)
1 mat H(2, 2)
Goto TRANS
Label SIMRATIO
Print "Input
SIMILITUDE RATIO
Input R
R K
K mat H(1, 1)
0 mat H(2, 1)
0 mat H(1, 2)
θ mat H(2, 2)
Goto TRANS
Label ROTATE
Print "Input ANGLE
Input A
A B
cos B mat H(1, 1)
sin B mat H(2, 1)
-sin B mat H(1, 2)
cos B mat H(2, 2)
Label TRANS
mat H mat D mat A
Print "mat A(1, 1)
Print mat A(1, 1)
Print "mat A(2, 1)
Print mat A(2, 1)
End
=
X'
Y'
() ()
X
Y
1 0
0 -1
() ()
(())()
()()
() ()()
1. Symmetric transformation to
x-axis (Case 1)
=
X'
Y'
X
Y
-1 0
01
2. Symmetric transformation to
y-axis (Case 2)
=
X'
Y'
X
Y
K0
0 K
3. Similar transformation with ratio of
similitude K around origin (Case 3)
=
X'
Y'
X
Y
cos B -sin B
sin B cos B
4. Transformation revolving around
only angle B at the origin (Case 4)
s = 1
To label YSYMMETRY
s = 2
Y
Y
N
To label SYMRATIO
s = 3
Y
N
To label ROTATE
Label XSYMMETRY
Label YSYMMETRY
Transformation data set
Transformation data set
Label SIMRATIO
Label ROTATE
Entry of ratio of similitude
Entry of angle
Data set of transformation
Coordinate transformation
Display of coordinates after transformation
Data set of transformation
s = 4
Y
N
N
TYPE
Data set of transformation by revolving
Entry of angle (A)
matH(1,1) = cos B, matH(2,1) = sin B,
matH(1,2) = -sin B, matH(2,2) = cos B,
Matrix H multiplied by matrix D.
Coordinates displayed.
SIMRATIO
Data set of similar transformation
Entry of ratio of similitude (R)
matH(1,1) = K, matH(1,2) = 0,
matH(2,1) = 0, matH(2,2) = θ
Title : LINE TRN
14