Geometria

Respostas

1) a) Ya – Yb = Ya – Yc = Yb – Yc Xa – Xb Xa – Xc Xb – Xc

-4 –b = 2 – (-2) = b -4 2 –n 2–(-2) -4-(-2)

1 = b – 4 -2 = b – 4 b = 2 -2

-4 -2 = 1 -6 = 1 -6 = 2 – n (-1) n = 8 2-n 2-n

b) 2 n 1 2 n 2b + (-2n) – 16 + 2b – 8 + 4n = 0 -4 b 1 -4 b -2 4 1 -2 4 2x + 4y – 24 = 0

c) y = 2/4 x – 6 y = -2 x + c c = 12

y = -4/2 x + c 8 = -2 (2) + c

y = -2x + 12 ( reduzida)

2x + y – 12 = 0 (geral)

d) y = 2/4 x – 6 D (2, -10)

y – yp = m (x – xp)

y – (-10) = 2/4 (x – 2)

y + 10 = 0,5 x – 1

y = 0,5 x – 11 (reduzida)

e) A (2, 8) D (2, -10)

y = ax + b

a = Yb – Ya a = -10 -8 a = 0 Xb - Xa 2 -2

8 = 0x + b y = 0x + 8 b = 8

inclinação r = 2/4 inclinação u = 0

tg Φ = mr – mu tg Φ = 2/4 tg Φ = 2/4 26,56º 1 + mr . mu 1

2) A (2 , 2 , -10 ) B (-10 , -10 , -2) C (x , 0 , 0)

(CA)² = (CB)²

(x-2)² + (0-2)² = (x + 10)² + (0+10)²

(x²+4x+4) + 4 = (x² + 20x +100) +100

4x = 20x + 200 -8

4x – 20x = 192

-16x = 192 (-1)

16x = 192

X = 12 C ( 12 , 0 , 0)

3) M ( 10 , 0 , 2 ) B ( 2 , 10 , 0 )