Linear Transformation - Sharp EL-9650 User Manual

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
1. Symmetric transformation to
x-axis (Case 1)
X' 1 0
=
Y' 0 -1
2. Symmetric transformation to
y-axis (Case 2)
X' -1 0
=
Y' 0 1
Start
Array declaration
Entry of coordinates (X,Y)
TYPE
Entry of type
Y
s = 1 To label XSYMMETRY
N
Y
s = 2
To label YSYMMETRY
N
Y
s = 3
To label SYMRATIO
N
Y
s = 4
N
Label XSYMMETRY
Transformation data set
Label SIMRATIO
Entry of ratio of similitude
Data set of transformation
Coordinate transformation
Display of coordinates after transformation
End
14
X
Y
X
Y
FLOWCHART
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
To label ROTATE
matH(1,1) = 1, matH(1,2) = 0,
matH(2,1) = 0, matH(2,2) = -1
YSYMMETRY
Data set of y-axis symmetric transformation
Label YSYMMETRY
matH(1,1) = -1, matH(1,2) = 0,
matH(2,1) = 0, matH(2,2) = 1
SIMRATIO
Transformation data set
Data set of similar transformation
Entry of ratio of similitude (R)
matH(1,1) = K, matH(1,2) = 0,
Label ROTATE
matH(2,1) = 0, matH(2,2) =
Entry of angle
Data set of transformation by revolving
Entry of angle (A)
Data set of transformation
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.
EL-9650/9600c Graphing Calculator
3. Similar transformation with ratio of
similitude K around origin (Case 3)
X' K 0 X
=
Y' 0 K Y
4. Transformation revolving around
only angle B at the origin (Case 4)
X' cos B -sin B
=
Y' sin B cos B
X
Y
PROGRAMME LIST
(MATRIX MODE)
Title : LINE TRNS
{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)
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