Chapter 3, Problem 1PP

(General math) a. Write a C++ program to calculate and display the value of the slope of the line connecting two points with the coordinates (3,7) and (8,12). Use the fact that the slope between two points with the coordinates $\left(x_1,y_1\right)and\left(x_2,y_2\right)is\left(y_2-y_1\right)/\left(x_2-x_1\right).$

b. How do you know the result your program produced is correct?

c. After verifying the output your program produces, modify it to determine the slope of the line connecting the points (2,10) and (12,6).

d. What do you think will happen if you use the points (2,3) and (2,4), which results in a division by zero? How do you think this situation can be handled?

e. If your program doesn’t already do so, change its output to this:

The value of the slope is xxx.xx

The xxx.xx denotes placing the calculated value in a field wide enough for three places to the left of the decimal point and two places to the right of it.

Program Plan Intro

Program plan: -

Variables

used in the following program are given below: -

• line_slope: -To store the slope of the line
• a1, a2: - To store the coordinates point values of x1 and x2.
• b1, b2: - To store the coordinate point values of y1 and y2.

Formula used: - (b2 − b1)/(a2 − a1)

Program description: -The purpose of the C++ program is to determine the slope of the line connecting two points with the coordinates (3, 7) and (8, 12).

Program Description Answer

1

Explanation of Solution

Given information:

The slope between two points with the coordinates $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ is $\left(y_2-y_1\right)/\left(x_2-x_1\right)$

Program:

//header file
#include <iostream>
//using the namespace
usingnamespacestd;
intmain()
{
//declaring the variables
floatline_slope, a1 =3, a2 =8, b1 =7, b2 =12;
//calculating the slope of the line connecting two points
line_slope=(b2 - b1)/(a2 - a1);
//displaying the slope of the line_slope
cout<<"Slope of a line is: "<<line_slope<<endl;
//return statement
return0;
}

Explanation:

The above code is used to calculate the slope of a line connecting the two points.

Firstly, declaring the variables of float data type. The variable line_slope will store the slope of the line, a1, a2 and b1, b2 is used to store the coordinates point values of x1, x2 and y1, y2.

The slope of a line is calculated by the given formula $\left(y_2-y_1\right)/\left(x_2-x_1\right)$ .

Sample output: -

  

Program Plan Intro

To verify the result of the program is correct.

Explanation of Solution

Given information: formula to calculate the slope: - $\left(y_2-y_1\right)/\left(x_2-x_1\right)$

Slope of the line is 1

Explanation:

Now, calculating the slope of the line by manual calculating to verify the result of the above program.

  $\begin{array}{c}\text{slope}=\left(y_2-y_1\right)/\left(x_2-x_1\right)\\ =5/5\\ =1\end{array}$

Since, the slope of the line is 1.

Hence, verified

Program Plan Intro

To modify the program of exercise by changing the value of coordinates point values.

Explanation of Solution

Given information:formula to calculate the slope: - $\left(y_2-y_1\right)/\left(x_2-x_1\right)$

a1 = 2, a2 = 12 and b1 = 10, b2 = 6

Program:

//header file
#include <iostream>
//using the namespace
usingnamespacestd;
intmain()
{
//declaring the variables
floatline_slope, a1 =2, a2 =12, b1 =10, b2 =6;
//calculating the slope of the line connecting two points
line_slope=(b2 - b1)/(a2 - a1);
//displaying the slope of the line_slope
cout<<"Slope of a line is: "<<line_slope<<endl;
//return statement
return0;
}

Sample output: -

  

Explanation:

The slope of a line is calculated by same formula as used in the exercise 1.a$\left(y_2-y_1\right)/\left(x_2-x_1\right)$

In the above program only the value of the coordinates point has changed.

Program Plan Intro

To determine the situation while using the points (2, 3) and (2, 4) and the denominator part becomes zero.

Explanation of Solution

Given information:New coordinates point values: - (2, 3) and (2, 4)

Explanation:

While calculating the slope of a line where the coordinates point values are (2, 3) and (2, 4)thanthe values of x1, and x2 are 2 same and the values of y1, and y2 are 3 and 4,here the denominator value is zero as the expression (x2-x1) is equal to zero.

In this case, the value of the slope will be infinite. This situation can be handled by using a conditional statement given below: -

//header file
#include <iostream>
//using the namespace
usingnamespacestd;
intmain()
{
//declaring the variables
floatline_slope, a1 =2, a2 =2, b1 =3, b2 =4;
//calculating the slope of the line connecting two points
line_slope=(b2 - b1)/(a2 - a1);
//displaying the slope of the line_slope
cout<<"Slope of a line is: "<<line_slope<<endl;
//to check when the denominator is equal to zero
if((a2 - a1 ==0))
{
	//message
	cout<<"The slope of the line is infinite."<<endl;
}
//return statement
return0;
}

Sample output: -

  

Program Plan Intro

To make changes in the above program so that the output is produced in the given format: xxx.xx

cout<<"|"<<setw(5)<<setiosflags(ios::fixed)<<setprecision(2)<<5.267<<"|";

Explanation of Solution

Given information:The format of the output is xxx.xx

Program:

#include <iostream>
#include <iomanip>
//using the namespace
//for using the standard I/O 
usingnamespacestd;
intmain()
{
//declaring the variables
	//as per the requirement
floatline_slope, a1 =12, a2 =7, b1 =8, b2 =3;
//calculating the slope
	//by usinf the given formula
line_slope=(b2 - b1)/(a2 - a1);
//displaying the slope and settingthe format of output as xx.xxx
//the width is set to 6 and the number of digits after decimal is //set //to 2
cout<<"The value of the slope is "<<setw(6)<<setiosflags(ios::fixed )<<setprecision(2)<<line_slope<<endl;
//return statement
return0;
}

Sample output: -