Question

Determine a distancia entre a reta r:12x-5y+10 e o ponto p(3,1)

Answer 1

12x - 5y + 10 = 0
- 5y = - 12x - 10
y = 12x + 10 / 5

a = 12/5

12/5 . a = - 1
12a = - 5
a = - 5 / 12

- 5 / 12 = y - 1 / x - 3
12y - 12 = - 5x + 15
12y = - 5x + 27
y = - 5x + 27 / 12

12x + 10 / 5 = - 5x + 27 / 12
- 25x + 135 = 144x + 120
- 25x - 144x = 120 - 135
169x = 15
x = 0,088

y = - 5x + 27 / 12
y = - 5 (0,088) + 27 / 12
y = - 0,443 + 27 / 12
y = 26,556 / 12
y = 2 , 21

I ( 0,088 , 2,21 )

IP² = ( 3 - 0,088 )² + ( 1 - 2,21 )²
IP² = ( 2,912)² + ( - 1,21 )²
IP² = 8,479 + 1,4641
IP² = 9,9431
IP = 3 , 1532

============ > 3,1532.espero ter ajudado