The Museum of HP Calculators


Intersection of Line and Line for the HP-33E/C

This program is Copyright © 1978 by Hewlett-Packard and is used here by permission. This program was originally published in "HP-33E Mathematics Applications".

This program is supplied without representation or warranty of any kind. Hewlett-Packard Company and The Museum of HP Calculators therefore assume no responsibility and shall have no liability, consequential or otherwise, of any kind arising from the use of this program material or any part thereof.

Overview

This program calculates the point of intersection (xp, yp) of two lines, each of them is specified by two points i.e., (x1, y1), (x1', y1') and (x2, y2), (x2', y2'). xp and yp are calculated from the equation of straight line y = x tan theta+ c. i.e. by solving:

      | 1  -tan theta1 |  | yp |   | c1 |
      | 1  -tan theta2 |  | xp | = | c2 |  

"Error 0" will be displayed if two lines have the same slope, i.e. if they are either parallel or overlapping.

Instructions

Step

Instructions

Input Data/Units

Keys

Output Data/Units

1

Enter program

     

2

Input the first line by two points

x1

ENTER

 

 

 

x1'

ENTER

 

   

y1

ENTER

 

 

 

y1'

GSB 01

C1

3

Input the 2nd line by two points and calculate the intersection.

 x2

ENTER

 

 

 

x2'

ENTER

 

 

 

y2

ENTER

 

   

y2'

GSB 10

xp

     

R/S

yp

4

For a new pair of lines, go to step 2.

 

 

 

Example

Find the intersection of the lines defined by the points (4, 8), (-1, -2) and (-3, 9), (7, -1).

Solution:

xp = 4, yp = 2

Keystrokes        Display
4 ENTER 1
CHS ENTER 8
ENTER 2 CHS
GSB 01            0.0000
3 CHS ENTER 7
ENTER 9 ENTER 1
CHS GSB 10        4.0000
R/S               2.0000

The Program

LINE    CODE    KEYS
 00             f CLEAR PRGM
 01     12 37   GSB 37
 02     23  3   STO 3
 03     24  2   RCL 2
 04     24  1   RCL 1
 05     24  3   RCL 3
 06        61   x
 07        41   -
 08     23  4   STO 4
 09        74   R/S
 10     12 37   GSB 37
 11     23  5   STO 5
 12     24  2   RCL 2
 13     24  1   RCL 1
 14     24  5   RCL 5
 15        61   x
 16        41   -
 17     23  6   STO 6
 18     24  4   RCL 4
 19        41   -
 20     24  3   RCL 3
 21     24  5   RCL 5
 22        41   -
 23     23  7   STO 7
 24        71   ÷
 25        74   R/S
 26     24  4   RCL 4
 27     24  5   RCL 5
 28        32   CHS
 29        61   x
 30     24  3   RCL 3
 31     24  6   RCL 6
 32        61   x
 33        51   +
 34     24  7   RCL 7
 35        71   ÷
 36        74   R/S
 37     23  1   STO 1
 38        41   -
 39     23  0   STO 0
 40        22   Roll dn
 41     23  2   STO 2
 42        41   -
 43     24  0   RCL 0
 44     15  4   g ->P
 45        22   Roll dn
 46     14  9   f TAN
 47     15 12   g RTN

Register Use

R0  used
R1  x1', x2'
R2  y1', y2'
R3  tantheta1
R4  c1
R5  tantheta2
R6  C2
R7  Det

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