5.18. 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
c are all integers. The slope of an APLine is defined to be the double value
-a / b . A point (represented by integers
y) is on an APLine if the equation of the APLine is satisfied when those
y values are substituted into the equation. That is, a point represented by
y is on the line if
ax + by + c is equal to 0. Examples of two APLine equations are shown in the following table.
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
5.18.1. Try and Solve It¶
Write the APLine class. Your implementation must include a constructor that has three integer parameters that represent
c, in that order.
You may assume that the values of the parameters representing
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 (
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).