The equation of a line in standard form is ax + by = c , where a and b both cannot be zero, and a , b , and c are real numbers. If b ≠ 0, then −a / b is the slope of the line. If a = 0, then it is a horizontal line, and if b = 0, then it is a vertical line. The slope of a vertical line is undefined. Two lines are parallel if they have the same slope or both are vertical lines. Two lines are perpendicular if either one of the lines is horizontal and another is vertical, or if the product of their slopes is −1. Design the class lineType to store a line. To store a line, you need to store the values of a (coefficient of x ), b (coefficient of y ), and c . Your class must contain the following operations:
a. If a line is nonvertical, then determine its slope.
b. Determine if two lines are equal. (Two lines a 1 x + b 1 y = c 1 and a 2 x + b 2 y = c 2 are equal if either a 1 = a 2 , b 1 = b 2 , and c 1 = c 2 or a 1 = ka 2 , b 1 = kb 2 , and c 1 = kc 2 for some real number k .)
c. Determine if two lines are parallel.
d. Determine if two lines are perpendicular.
e. If two lines are not parallel, then find the point of intersection.
Add appropriate constructors to initialize variables of lineType . Also write a program to test your class.
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