6.17. Free Response Question - APLine¶
The following is a free response question from 2010. It was question 2 on the exam. You can see all the free response questions from past exams at https://apstudents.collegeboard.org/courses/ap-computer-science-a/free-response-questions-by-year.
Question 2. An APLine is a line defined by the equation ax + by + c = 0
,where a
is not equal to zero, b
is not equal to
zero, and a
, b
, and c
are all integers. The slope of an APLine is defined to be the double value -a / b
. A point (represented by integers x
and y
) is on an APLine if the equation of the APLine is satisfied when those x
and y
values are substituted into the equation. That is, a point represented by x
and y
is on the line if
ax + by + c
is equal to 0. Examples of two APLine equations are shown in the following table.
![../_images/apLineTable.png](../_images/apLineTable.png)
Assume that the following code segment appears in a class other than APLine. The code segment shows an example of using the APLine class to represent the two equations shown in the table.
APLine line1 = new APLine(5, 4, -17);
double slope1 = line1.getSlope(); // slope1 is assigned -1.25
boolean onLine1 = line1.isOnLine(5, -2); // true because 5(5) + 4(-2) + (-17) = 0
APLine line2 = new APLine(-25, 40, 30);
double slope2 = line2.getSlope(); // slope2 is assigned 0.625
boolean onLine2 = line2.isOnLine(5, -2); // false because -25(5) + 40(-2) + 30 != 0
6.17.1. Try and Solve It¶
Write the APLine class. Your implementation must include a constructor that has three integer parameters that represent a
, b
, and c
, in that order.
You may assume that the values of the parameters representing a
and b
are not zero.
It must also include a method getSlope()
that calculates and returns the slope of the line (using the equation -a / b
) and a method isOnLine(x, y)
that returns true
if the point represented by its two parameters (x
and y
, in that order) is on the APLine
and returns false
otherwise, by testing if
ax + by + c
is equal to 0.
Your class must produce the indicated results when the main method below is run. You may ignore any issues related to integer overflow.
Write a class APLine with instance variables, a constructor with 3 paramaters for a, b, c, and the methods getSlope() and isOnLine(x,y).