TI-84 Plus: Intersection of two lines – program by Jack
Kesler
Special thanks
to Jack Kessler for providing the program CPXINT. CPXINT uses complex numbers to determine:
* The equation
of a line between two points. CPXINT
uses two lines:
y = Ax + B for coordinates N1, E1
and N2, E2.
y = Cx + D for coordinates N3, E3
and N4, E4
* The
intersection of the two lines, labeled by point N5, E5.
Keep in mind N
is for North (y axis) and E is for East (x axis).
TI-84 Plus Program CPXINT – Jack Kesler
Note: Initialize all the variables by choosing
option 1, SETUP. Choose 2 for input, 3
for equations of the lines, and 4 for intersection.
ClrHome
Disp "LINE
INT"
Disp "USNG
CPX"
Disp "VER.
1.0"
Pause
ClrHome
Lbl 50
Menu("CPXINT","SETUP",89,"INP
PTS",90,"COMP LINS",91,"COMP
INT",92,"EXIT",93)
End
Lbl 89
ClrHome
ClrAllLists
11→dim(L₁)
{2,2}→dim([A])
{2,1}→dim([B])
Goto 50
Lbl 90
ClrHome
Disp "INP
CRDS:"
Input "N1=
",T
T→L₁(1)
Input "E1=
",T
T→L₁(2)
Input "N2=
",T
T→L₁(3)
Input "E2=
",T
T→L₁(4)
Input "N3=
",T
T→L₁(5)
Input "E3=
",T
T→L₁(6)
Input "N4=
",T
T→L₁(7)
Input "E4=
",T
T→L₁(8)
ClrHome
Goto 50
Lbl 91
ClrHome
a+bi
L₁(2)+L₁(1)i→I
L₁(4)+L₁(3)i→J
angle(J-I)→θ
If θ=90 or θ=90
Then
real(I)→B
0→[A](1,1)
1→[A](1,2)
B→[B](1,1)
0→A
Else
tan(θ)→A
imag(I)-A*real(I)→B
1→[A](1,1)
A→[A](1,2)
B→[B](1,1)
End
Disp
"Y=A*X+B"
Disp "A=
",A
Disp "B=
",B
Pause
ClrHome
L₁(6)+L₁(5)i→I
L₁(8)+L₁(7)i→J
angle(J-I)→θ
If θ=90 or θ=90
Then
real(I)→D
0→[A](2,1)
1→[A](2,2)
D→[B](2,1)
0→C
Else
tan(θ)→C
imag(I)-C*real(I)→D
1→[A](2,1)
C→[A](2,2)
D→[B](2,1)
End
Disp
"Y=C*X+D"
Disp "C=
",C
Disp "D=
",D
Pause
ClrHome
Real
Goto 50
Lbl 92
ClrHome
If A=C
Then
Disp "PARLLEL
LINES"
Disp "NO
SOLUTION"
Pause
ClrHome
Goto 50
End
[A]^-1*[B]→[D]
Disp "N5=
",[D](1,1)
[D](1,1)→L₁(9)
Disp "E5=
",[D](2,1)
[D](2,1)→L₁(10)
Pause
ClrHome
Goto 50
Lbl 93
ClrHome
Stop
Example:
Line 1: N1 = 0, E1 = 1, N2 = 7, E2 = 2.
Line 2: N3 = 4, E3 = 3, N4 = 4, E3 = -3
Results:
Y = AX +
B: A = 0, B = 4
Y = CX +
D: C = 7, D = -7
Intersection: N5 = 4,
E5 = 1.571428571
Thank you
Jack!
Eddie
This blog is
property of Edward Shore, 2016
