**HP 35S: Intersection Point of a Quadrilateral**

**Introduction**

Let A, B, C, and D be four vertices of a quadrilateral, with
two lines:

Line AC connects points A and C.

Line BC connects points B and D.

Designate the following points as:

A: (ax, ay)

B: (bx, by)

C: (cx, cy)

D: (dx, dy)

The center point (px, py) can be found by the following
formulas:

px = (IBD – IAC)/(SAC – SBD)

py = SAC * px + IAC

Where:

Slope:

SAC = (cy – ay) / (cx – ax)

SBD = (dy – by) / (dx – bx)

Intercept:

IAC = ay – SAC * ax

IBD = by – SBD * bx

You can see the derivation of these formulas here: https://edspi31415.blogspot.com/2017/08/geometry-intersection-point-of.html

**Program**(Pedro Daniel Leiva)

The following program calculates the point – developed by Pedro
Daniel Leiva. I used the recall arithmetic available on the HP 35S to shorten
the program. Program listed here with
permission.

Variables Used:

R_A = ax

R_B = ay

R_C = bx

R_D = by

R_E = cx

R_F = cy

R_G = dx

R_H = dy

R_I = SAC

R_J = SBD

R_K = IAC

R_L = IBD

R_P = px

R_Y = py

Program:

I001 LBL I

I002 SF 10

I003 ENTER
XA^YA \\ EQN

I004 STO B

I005 x<>y

I006 STO A

I007 ENTER
XB^YB \\ EQN

I008 STO D

I009 x<>y

I010 STO C

I011 ENTER XC^YC \\
EQN

I012 STO F

I013 x<>y

I014 STO E

I015 ENTER
XD^YD \\ EQN

I016 STO H

I017 x<>y

I018 STO G

I019 CF 10

I020 RCL F

I021 RCL - B \\ [RCL] [ - ] ( B )

I022 RCL E

I023 RCL - A \\ [RCL] [ - ] ( A )

I024 ÷

I025 STO I

I026 STO P \\ advanced storage to calculate px to save
steps

I027 RCL× A

I028 +/-

I029 RCL+ B

I030 STO K

I031 RCL H

I032 RCL - D

I033 RCL G

I034 RCL – C

I035 ÷

I036 STO J

I037 STO – P

I038 RCL × C

I039 +/-

I040 RCL + D

I041 STO L

I042 RCL – K

I043 RCL ÷ P

I044 STO P

I045 ENTER

I046 RCL × I

I047 RCL + K

I048 STO Y

I049 x<>y

I050 RTN

50 steps

Instructions:

At each prompt, enter the x point, press [ENTER], enter the
y point, press [ R/S ]. The result shows
py on the Y stack, and px on the X stack.

Example:

A: (0, 8)

B: (11, 12)

C: (10, 4)

D: (3, 5)

Results:

py = 6.2353

px = 4.4118

Eddie

All original content copyright, ©
2011-2018. Edward Shore. Unauthorized use and/or unauthorized
distribution for commercial purposes without express and written permission
from the author is strictly prohibited.
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that full credit is given to the author.
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