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 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.

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 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).

// Declare the APLine class

{
 /** Declare instance variables */

/** Constructor with 3 int parameters. */

/** method getSlope(): Determine the slope of this APLine. */

/** method isOnLine(x,y): Determine if coordinates (x,y) represent a point on this APLine. */

/** Test with this main method */
 public static void main(String[] args)
 {
     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
     // Should print out true and false
     System.out.println(onLine1 + " " + onLine2);
  }
}
====
// Test Code for Lesson 5.15 - FRQ - APLine
import static org.junit.Assert.*;

import org.junit.Test;

import java.io.*;

public class RunestoneTests extends CodeTestHelper
{
    public RunestoneTests()
    {
        super("APLine");
        // This sets default values for when objects are instantiated
        Object[] values = new Object[] {3, 2, -6};
        setDefaultValues(values);
    }

@Test
    public void testMain() throws IOException
    {
        String output = getMethodOutput("main");
        String expect = " true false";

boolean passed = getResults(expect, output, "Running main");
        assertTrue(passed);
    }

@Test
    public void testConstructor()
    {
        String output = checkConstructor(3);
        String expect = "pass";

boolean passed = getResults(expect, output, "Checking constructor with 3 parameters");
        assertTrue(passed);
    }

@Test
    public void testGetSlope() throws IOException
    {
        double output = Double.parseDouble(getMethodOutput("getSlope"));
        double expect = -1.5;

boolean passed = getResults(expect, output, "Checking method getSlope()");
        assertTrue(passed);
    }

@Test
    public void testIsOnLine1() throws IOException
    {
        Object[] args = {2, 0};
        String output = getMethodOutput("isOnLine", args);
        String expect = "true";

boolean passed = getResults(expect, output, "Checking method isOnLine(5, -2)");
        assertTrue(passed);
    }

@Test
    public void testIsOnLine2() throws IOException
    {
        Object[] args = {5, -2};
        String output = getMethodOutput("isOnLine", args);
        String expect = "false";

boolean passed = getResults(expect, output, "Checking method isOnLine(5, -2)");
        assertTrue(passed);
    }

@Test
    public void testPrivateVariables()
    {
        String expect = "3 Private";
        // Will produce a printout with number of private and public variables
        String output = testPrivateInstanceVariables();

boolean passed = getResults("3 Private", output, "Checking Instance Variable(s)");

assertTrue(passed);
    }
}

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