Self-Assessment Solutions

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The Point Defined

1.

A(2,1), B( “1, “3), C( “3,0), D(0,3), E(3, “3)

2.

The answer is shown in Figure 1.21.

Figure 1.21. Graph of points A through E.

graphics/01fig21.gif

3.

( “2,1, “4)

4.

(2,3,2)


The Line Defined

1.

Yes

2.

Yes

3.

Yes

4.

No


5.

The answer is shown in Figure 1.22.

Figure 1.22. Graph of x “ 2y = 0.

graphics/01fig22.gif

6.

The answer is shown in Figure 1.23.

Figure 1.23. Graph of “3x + y = 4.

graphics/01fig23.gif

7.

The answer is shown in Figure 1.24.

Figure 1.24. Graph of x = 1.

graphics/01fig24.jpg


Properties of Lines

1.

m = “2

2.

m = “2

3.

m = ½

4.

m = 3

5.

m = 3/2

6.

m = undefined

7.

m = ½

8.

m = 0

9.

They are parallel.

10.

Vertical

11.

Horizontal


12.

m = “2/3

13.

m = 1/5

14.

m = 0

15.

m = “1


16.

( y “10) = “2( x ) or y = “2 x + 10

17.

( y “5) = “2( x “3) or y = “2 x + 11

18.

( y +1) = ½( x “2) or y = ½ x “ 2

19.

( y “4) = 3( x “1) or y = 3 x + 1

20.

point <2,0, “1> and vector <1,4,6>

21.

point < “3,1,5> and vector <3,7, “7>


Applications in Collision Detection

1.

m 1 = “1, b 1 = 7, m 2 = 1/3 , b 2 = 2/3 ; one solution

2.

m 1 = 1/3 , b 1 = 2, m 2 = 1/3 , b 2 = “2; zero solutions

3.

m 1 = “ ¼, b 1 = 2, m 2 = “ ¼, b 2 = 2; infinite solutions

4.

m 1 = 1, b 1 = “5, m 2 = “5, b 2 = 0; one solution

5.

m 1 = “ 1/3 , b 1 = “ 1/3 , m 2 = “ 1/3 , b 2 = “ 5/6 ; zero solutions

6.

m 1 = 3/5 , b 1 = graphics/01inl04.gif , m 2 = “ 3/5 , b 2 = graphics/01inl04.gif ; one solution


7.

(2,1)

8.

(6,0)


9.

(0,3)

10.

(5, “4)


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Beginning Math and Physics for Game Programmers
Beginning Math and Physics for Game Programmers
ISBN: 0735713901
EAN: 2147483647
Year: 2004
Pages: 143
Authors: Wendy Stahler

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