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*8.30
(
Algebra: solve linear equations
) Write a method that solves the following
2
*
2 system of linear equations:
+
=
b
0
a
11
-
b
1
a
01
b
1
a
00
-
b
0
a
10
a
00
x
a
01
y
b
0
=
=
x
y
+
=
a
00
a
11
-
a
01
a
10
a
00
a
11
-
a
01
a
10
a
10
x
a
11
y
b
1
The method header is
public static double
[] linearEquation(
double
[][] a,
double
[] b)
The method returns
null
if
a
00
a
11
a
01
a
10
is
0
. Write a test program that
prompts the user to enter
a
00
,
a
01
,
a
10
,
a
11
,
b
0
, and
b
1
, and displays the result. If
a
00
a
11
-
a
01
a
10
is
0
, report that “The equation has no solution.” A sample run is
similar to Programming Exercise 3.3.
-
*8.31
(
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 inter-
secting 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 Program-
ming Exercise 3.25 for a sample run.
*8.32
(
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 computed using the
formula in Programming Exercise 2.19. The method returns
0
if the three points
are on the same line. Write a program that prompts the user to enter three points of
a triangle and displays the triangle's area. Here is a sample run of the program:
Enter x1, y1, x2, y2, x3, y3: 2.5 2 5 -1.0 4.0 2.0
The area of the triangle is 2.25
Enter x1, y1, x2, y2, x3, y3: 2 2 4.5 4.5 6 6
The three points are on the same line
*8.33
(
Geometry: polygon subareas
) A convex 4-vertex polygon is divided into four
triangles, as shown in Figure 8.9.
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
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