1. Basic -short question

1.

a) False: counter example Let x1=4, x2=1. =3, but x2 - x1= -3

b) True

c) True

d) True

2.

a)

b) Yes

c) The distance between(x1, y1) and (x2, y2) is the same as the distance betwen (x2, y2) and (x1, y1).

3.

a)

b) one example: (-4, 5) (-3, 6) (-2, 5) (-3, 4)

4. The distance formula

2. Application problem

1. Think of the path as beimg on a coordinate grid with Tom's place at (0, 0). Doris' house is at the point (1.75, 3.5). The air distance between them is the length of TD.

They are about 3.9 miles apart.

2. Lattice point is a point with integer coordinates. The graph is below.

3. 46, or 54, depending on which piece was cut from each end.

4. By midpoint formula, D=(3.5, 2.5). By distance formula, length of AD is .

3. Proof questions

1. BC=sqr root of 145 and BA =sqr root of 145. Thus, by the definition of circle (sufficient condition), C and A are on the same circle with center B.

2.

a) By midpoint formula, M=(11.5, 9.5), N=(20, 12), P=(14.5, 22,5), Q=(6, 20)

By distance formula, the length of MN is sqr root of 78.5, and the length of PQ is sqr root of 78.5. So The length of MN and PQ has the same length.

b) The slope of MN=2.5/8.5 and the slope of PQ = 2.5/8.5 by the definition of slope. So MN // PQ by the Parallel lines and slopes theorem.

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