CPTR 124 Fundamentals of Programming
In this lab you will write a module containing multiple functions that dabble in analytic geometry.
 Teams
You are encouraged to work with a partner for this lab. You and your partner should begin thinking about the problems and begin writing the code before lab time.
 What to do
In this assignment you will manage two Python source files:

geometry.py
. You will implement four of the functions specified in this file. We will defer one of the functions until the next assignment. More information about these functions appears below. This file constitutes thegeometry
module. 
testgeom.py
. This program uses yourgeometry
module, allowing a user to enter in the coordinates of two geometric points. The program then prints four things: the distance between the two points,
 the slope of the line that passes through the two points,
 the yintercept of the line that passes through the two points, unless the line is vertical; in which case the program prints the xintercept of the line, and
 the equation of the line (in slopeintercept form) that passes through the two points.
You should not modify this program.
geometry
Python module consisting of four functions that the other file will use. The program found intestgeom.py
will not work properly until you correctly implement the expected functions.The required functions are:
 distance
The distance between two points (x_{1}, y_{1}) and (x_{2}, y_{2}), is given in the following formula:
Write a function named
distance
that accepts four floatingpoint arguments x_{1}, y_{1}, x_{2}, and y_{2}, in that order, representing two geometric points (x_{1}, y_{1}), and (x_{2}, y_{2}). It should return the floatingpoint value representing the distance between the two points. You can compute the square root of a numeric value via thesqrt
function in the standardmath
module.  slope
The slope of the line passing through two points (x_{1}, y_{1}) and (x_{2}, y_{2}), is the difference of the y values divided by the difference of the x values:
Write a function named
slope
that accepts four floatingpoint arguments and returns the floatingpoint value representing the slope of the line passing through the two points represented by the arguments.Watch out for vertical lines! Return the value
inf
to represent infinity if the line is vertical. Theinf
value is defined in the standardmath
module.Note: The function's behavior is undefined for parameters that represent two equal points. When we say the function's behavior is undefined, we mean you do not need to worry about what your function does if the client attempts to compute the slope with two points that are the same. (Later in this course we will consider how to properly handle such exceptional situations.)
 intercept
An intercept is a number that represents a location on an axis where a line intersects that axis. The yintercept of a line is the y value of the point where a line crosses the yaxis. Write a function named
intercept
that accepts four floatingpoint arguments representing the coordinates of two points. The function ordinarily returns the floatingpoint value representing the yintercept of the line that that passes through the two points defined by the arguments.For nonvertical lines, we can compute the yintercept from the y = mx + b form of a line. Solving for b, we get b = y  mx:
This means if we know the slope, m, we can plug in the (x, y) coordinates from either point to compute b.
Vertical lines do not have a yintercept, so the
intercept
function instead should return the xintercept for vertical lines. If the two points form a vertical line, it is easy to determine the xintercept.Note: The function's behavior is undefined for parameters that represent two equal points. Again, this means you need not worry about this possibility in your function.
 intersection
You do not need to implement this function at this time. You will implement it for the next assignment.
 lineequation
The equation of a line in slopeintercept form is
y = mx + b where m is the line's slope, and b is the line's y intercept.Write a function named
lineequation
that accepts four floatingpoint arguments representing coordinates of two points. It should return a text string expressing the equation of that line in slopeintercept form.A vertical line has an equation of the form
x = b
where b is the xintercept. Your function should produce the equation for vertical lines correctly.
When creating the string round all displayed numbers to two decimal places. The equation your function produces should be "pretty," meaning do not return an equation like
y = 1.0x + 3.0rather the function should return the stringy = x  3.0and an equation likey = 20.5x + 0.0should appear asy = 20.5xPlace spaces around the equals symbol and the addition and subtraction symbols so the equation appears as you might see it in a mathematics textbook. This means you will need some conditional statements within yourlineequation
function to fine tune the exact representation.It is important to note that in your
lineequation
function you are not printing anything; instead, you are building a string that code withintestgeom.py
will print. Start with the empty string (""
) and concatenate the string"y = "
or"x = "
depending on whether the line is vertical or not. Then concatenate the appropriate slope and intercept values as appropriate. Recall that you cannot concatenate a string and a number directly. Ifeqn
is the equation string you are building andm
is a variable bound to the floatingpoint value 2.0, to build the string"y = 2.0x"
you would need to writeeqn = "y = " + str(m)
in Python.As you begin developing your
lineequation
function do not worry about pretty formatting. First concentrate on getting the numbers correct, and after you are sure the results are mathematically sound then, if you have time, proceed to make the representation more attractive.If you do not have the time or interest to make the string "pretty," you may elect to receive 9/10 points for the assignment if your string is just mathematically correct.
 floatequals
I have provided the
floatequals
function for you to use as needed. Remember that many floatingpoint numbers do not have an exact representation. This means the==
operator may consider two floatingpoint numbers unequal even though we believe they should be equal. The graphical user interface functions are limited to the pixel size based on the screen resolution. Thefloatequals
function can help adjust for the graphical environment's limitations.

 Organization
Copy the files
geometry.py
andtestgeom.py
to the same folder (or directory). Do not change the names of the files.Your task is to complete the functions (except for
intersection
) ingeometry.py
. Do not touch any of the code intestgeom.py
.Unlike all the previous programming assignments, the code you write is not in control. The code provided for you is in control, and your code must be able to react to it appropriately.
It is important that you not include any
print
orinput
statements within your functions. The code withintestgeom.py
is responsible for obtaining input from the user and displaying the results. Also, yourdistance
,slope
, andintercept
functions should perform no rounding. Callers can round the results you compute as they see fit. It is appropriate to round the floatingpoint values that you use to build the line equation string in yourlineequation
function—round these to two decimal places.  Strategy
First download the two Python source files. Before you touch the code in
geometry.py
make sure that thetestgeom.py
program executes without any runtime exceptions. Since you have yet to add your code to thegeometry
module, the program will not work correctly, but it should not crash. The filegeometry.py
contains five function stubs. They each return some default value that clients are able to use without crashing.To keep things simpler to begin with, don't worry about handling vertical lines and don't worry about "pretty" equation output. Make sure your code works properly with
testgeom.py
with simple, limited examples. After everything works under those restricted conditions, then implement vertical line capability and afterwards pretty output.Note that to execute your program within the Wing IDE the
testgeom.py
editor window must be the active editor window. If you attempt to run the program with thegeometry.py
file active, the program will not run. So, edit (but do not run) thegeometry.py
file, and run (but do not edit) thetestgeom.py
file.  Check out
Double check to make sure your
distance
,slope
, andintercept
functions are returning numbers, not strings and that they are doing no rounding. Yourlineequation
function should return a string.Your finished module will be evaluated for correctness and compliance. When approved, you should submit your
geometry.py
Python source file to http://eclass.e.southern.edu. Be sure your name and your partner's name are included in comments in the first line of your source file.