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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
¼
c
1
and a
2
x + b
2
y
¼
c
2
are equal if either a
1
¼
a
2
, b
1
¼
b
2
, and c
1
¼
c
2
or a
1
¼
ka
2
, b
1
¼
kb
2
, and
c
1
¼
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
Line
. Also write a
program to test your class.
8.
Rational fractions are of the form a / b,wherea and b are integers and b
6¼
0.
In this exercise, by ''fractions'' we mean rational fractions. Suppose that a / b and
c / d are fractions. Arithmetic operations on fractions are defined by the following
rules:
a / b + c / d
¼
(ad + bc)/bd
a / b - c / d
¼
(ad - bc)/bd
a / b
c / d
¼
ac / bd
(a / b)/(c / d)
¼
ad / bc, where c / d
6¼
0
Fractions are compared as follows: a / bopc/ d if ad op bc, where op is any of
the relational operations. For example, a / b
<
c / d if ad
<
bc.
Design the
class
Fraction
that can be used to manipulate fractions in a
program. Among others, the
class
Fraction
must include methods to add,
subtract, multiply, and divide fractions. When you add, subtract, multiply, or
divide fractions, your answer need not be in the lowest terms. Also, override the
method
toString
so that the fractions can be output using the output statement.
Write a Java program that, using the
class
Fraction
, performs operations on
fractions.
8
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