Sharp EL-9900 Linear Transformation, XY = 10 -01 XY, XY = -01 01 XY, XY = K0 K0 XY, Calculation

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

1.Symmetric transformation to x-axis (Case 1)

(X'Y') = ( 10 -01) ( XY)

2.Symmetric transformation to y-axis (Case 2)

( X'Y') = ( -01 01 ) ( XY)

3.Similar transformation with ratio of similitude K around origin (Case 3)

(X'Y') = (K0 K0 ) ( XY )

4.Transformation revolving around only angle B at the origin (Case 4)

( X') = ( cos B		-sin B) (	X)
Y'	sin B	cos B	Y

FLOWCHART		PROGRAMME LIST
	Title : LINE TRN

Start

Array declaration

Entry of coordinates (X,Y)

TYPE

Entry of type

s = 1		Y	To label XSYMMETRY
	N	Y
s = 2			To label YSYMMETRY
	N	Y
s = 3			To label SYMRATIO
	N	Y
s = 4			To label ROTATE
	N

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

{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)

Label XSYMMETRY

Transformation data set

Label SIMRATIO

Entry of ratio of similitude

Data set of transformation

Label YSYMMETRY

Transformation data set

Label ROTATE

Entry of angle

Data set of transformation

Data set of y-axis symmetric transformation matH(1,1) = -1, matH(1,2) = 0, matH(2,1) = 0, matH(2,2) = 1

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

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,

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)

Coordinate transformation

Display of coordinates after transformation

End

Matrix H multiplied by matrix D.

Coordinates displayed.

cos B mat H(2, 2)

Label TRANS

mat Hmat D mat A Print "mat A(1, 1) Print mat A(1, 1) Print "mat A(2, 1) Print mat A(2, 1)

End

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