Self-Assessment Solutions

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.
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.
6.	The answer is shown in Figure 1.23. Figure 1.23. Graph of –3x + y = 4.
7.	The answer is shown in Figure 1.24. Figure 1.24. Graph of x = 1.

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 = –2x + 10
17.	(y–5) = –2(x–3) or y = –2x + 11
18.	(y+1) = ½(x–2) or y = ½x – 2
19.	(y–4) = 3(x–1) or y = 3x + 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.	m1 = –1, b1 = 7, m2 = 1/3, b2 = 2/3; one solution
2.	m1 = 1/3, b1 = 2, m2 = 1/3, b2 = –2; zero solutions
3.	m1 = –¼, b1 = 2, m2 = –¼, b2 = 2; infinite solutions
4.	m1 = 1, b1 = –5, m2 = –5, b2 = 0; one solution
5.	m1 = –1/3, b1 = –1/3, m2 = –1/3, b2 = –5/6; zero solutions
6.	m1 = 3/5, b1 = , m2 = –3/5, b2 = ; one solution

7.	(2,1)
8.	(6,0)

9.	(0,3)
10.	(5,–4)