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y
-axis
y
-axis
(9, 9)
(4, 5)
(6, 4)
(2, 2)
(0, 0)
x
-axis
(0, 0)
x
-axis
(a)
(b)
F
IGURE
3.7
(a) Points inside and outside of the circle. (b) Points inside and outside of the
rectangle.
**3.23
(
Geometry: point in a rectangle?
) Write a program that prompts the user to enter
a point
(x, y)
and checks whether the point is within the rectangle centered at
(
0
,
0
) with width
10
and height
5
. For example, (
2
,
2
) is inside the rectangle and
(
6
,
4
) is outside the rectangle, as shown in Figure 3.7b. (
Hint
: A point is in the
rectangle if its horizontal distance to (
0
,
0
) is less than or equal to
10 / 2
and its
vertical distance to (
0
,
0
) is less than or equal to
5.0 / 2
. Test your program to
cover all cases.) Here are two sample runs.
Enter a point with two coordinates: 2 2
Point (2.0, 2.0) is in the rectangle
Enter a point with two coordinates: 6 4
Point (6.0, 4.0) is not in the rectangle
**3.24
(
Game: pick a card
) Write a program that simulates picking a card from a deck
of
52
cards. Your program should display the rank (
Ace
,
2
,
3
,
4
,
5
,
6
,
7
,
8
,
9
,
10
,
Jack
,
Queen
,
King
) and suit (
Clubs
,
Diamonds
,
Hearts
,
Spades
) of the card.
Here is a sample run of the program:
The card you picked is Jack of Hearts
*3.25
(
Geometry: intersecting point
) Two points on line 1 are given as (
x1
,
y1
) and (
x2
,
y2
) and on line 2 as (
x3
,
y3
) and (
x4
,
y4
), as shown in Figure 3.8a-b.
The intersecting point of the two lines can be found by solving the following
linear equation:
(
y
1
-
y
2
)
x
-
(
x
1
-
x
2
)
y
=
(
y
1
-
y
2
)
x
1
-
(
x
1
-
x
2
)
y
1
x
4
)
y
3
This linear equation can be solved using Cramer's rule (see Programming Exer-
cise 3.3). If the equation has no solutions, the two lines are parallel (Figure 3.8c).
(
y
3
-
y
4
)
x
-
(
x
3
-
x
4
)
y
=
(
y
3
-
y
4
)
x
3
-
(
x
3
-
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