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 θ+ 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   ×
 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   ×
 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   ×
 30     24  3   RCL 3
 31     24  6   RCL 6
 32        61   ×
 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   R↓     
 41     23  2   STO 2
 42        41   -
 43     24  0   RCL 0
 44     15  4   g →P 
 45        22   R↓     
 46     14  9   f TAN
 47     15 12   g RTN

Register Use

R0  used
R1  x1', x2'
R2  y1', y2'
R3  tanθ1
R4  c1
R5  tanθ2
R6  C2
R7  Det

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