Java Reference
In-Depth Information
*7.30
(
Algebra: solve linear equations
) Write a method that solves the following
system of linear equations:
2
*
2
a
00
x
+
a
01
y
=
b
0
b
0
a
11
-
b
1
a
01
b
1
a
00
-
b
0
a
10
b
1
x
=
a
01
a
10
y
=
a
10
x
+
a
11
y
=
a
00
a
11
-
a
00
a
11
-
a
01
a
10
The method header is
public static double
[] linearEquation(
double
[][] a,
double
[] b)
The method returns
null
if is
0
. Write a test program that
prompts the user to enter and and displays the result. If
is
0
, report that “The equation has no solution.” A sample run is
similar to Programming Exercise 3.3.
a
00
a
11
-
a
01
a
10
a
00
,
a
01
,
a
10
,
a
11
,
b
0
,
b
1
,
a
00
a
11
-
a
01
a
10
*7.31
(
Geometry: intersecting point
) Write a method that returns the intersecting point of
two lines. The intersecting point of the two lines can be found by using the formula
shown in Programming Exercise 3.25. Assume that (
x1
,
y1
) and (
x2
,
y2
) are the
two points on line 1 and (
x3
,
y3
) and (
x4
,
y4
) are on line 2. The method header is
public static double
[] getIntersectingPoint(
double
[][] points)
The points are stored in a 4-by-2 two-dimensional array
points
with
(
points[0][0]
,
points[0][1]
) for (
x1
,
y1
). The method returns the intersect-
ing point or
null
if the two lines are parallel. Write a program that prompts the
user to enter four points and displays the intersecting point. See Programming
Exercise 3.25 for a sample run.
*7.32
(
Geometry: area of a triangle
) Write a method that returns the area of a triangle
using the following header:
public static double
getTriangleArea(
double
[][] points)
The points are stored in a 3-by-2 two-dimensional array
points
with
points[0][0]
and
points[0][1]
for (
x1
,
y1
). The triangle area can be com-
puted using the formula in Programming Exercise 2.15. The method returns
0
if the
three points are on the same line. Write a program that prompts the user to enter
two lines and displays the intersecting point. Here is a sample run of the program:
Enter x1, y1, x2, y2, x3, y3:
The area of the triangle is 2.25
2.5 2 5 -1.0 4.0 2.0
2 2 4.5 4.5 6 6
Enter x1, y1, x2, y2, x3, y3:
The three points are on the same line
*7.33
(
Geometry: polygon subareas
) A convex 4-vertex polygon is divided into four tri-
angles, as shown in Figure 7.9.
Write a program that prompts the user to enter the coordinates of four vertices and
displays the areas of the four triangles in increasing order. Here is a sample run:
Enter x1, y1, x2, y2, x3, y3, x4, y4:
-2.5 2 4 4 3 -2 -2 -3.5
The areas are 6.17 7.96 8.08 10.42
