1) The document provides instructions to calculate the distance between points, find the midpoint between points, and obtain the equation of a line passing through two points. 2) It gives examples of calculating the distance between several pairs of points and finding the midpoint between other pairs of points. 3) To obtain the equation of a line, it shows setting up the point-slope form using two points and solving the resulting system of equations.

1. RESOLUÇÃO DA AVALIAÇÃO
1) Calcular a distância.
a) (-5,4) e (2,-5)
D = √(2 − (−5))2 + (−5 − 4)2 = √(2 + 5)2 + (−9)2 = √72 + 81= √49 + 81= √130
b) (-1,5) e (-1,12)
D = √(−1 − (−1))2 + (5 − 12)2 = √(−1 + 1)2 + (−7)2 = √02 + 49 = √0 + 49= √49 = 7
c) (-4,3) e (-4,-7)
D = √(−4 − (−4))2 + (−7 − 3)2 = √(−4 + 4)2 + (−10)2 = √02 + 100 = √0 + 100= √100 =
10
d) (3,2) e (7,5)
D = √(3 − 7)2 + (2 − 5)2 = √(−4)2 + (−3)2 = √16 + 9 = √25 = 5
1) Calcular o ponto médio
a) (4,3) e (8,11)
Xm =
4+8
2
=
12
2
= 6 Ym =
11+3
2
=
14
2
= 7 (6,7)
b) (-4,-7) e (4,-4)
Xm =
−4+4
2
=
0
2
= 0 Ym =
−7−4
2
=
−11
2
(0,
−11
2
)
c) (6,1) e (-6,1)
Xm =
−6+(−6)
2
=
0
2
= 0 Ym =
1+1
2
=
2
2
= 1 (0,1)

2. 3) Obter a equação da reta que passa pelos pontos:
a) (2,0) e (4,1) x y 1 x y
2 0 1 2 0
4 1 1 4 1
-0 - x - 2y + 0 +4y + 2 = 0
- x - 2y +4y +2 = 0
-x + 2y + 2 =0
b) (3,4) e (7,4) x y 1 x y
3 4 1 3 4
7 4 1 7 4
- 28 – 4x – 3y +4x + 7y +12 = 0
- 4x + 4x – 3y + 7y – 28 + 12 = 0
0x + 4y – 16 = 0
4y – 16 = 0