Question

Calcule a altura relativa ao lado AC do triângulo de vértices A(1,2); B(3,5) e C(5,3)

Answer 1

RETA AC
;;;;:::;;;;;;;;;::

A(1,2) => Xa = 1 e Ya = 2
C(5,3) => Xc = 5 e Yc = 3

|..Xa...Ya...1..|
|..Xc...Yc...1..|
|...X......Y...1..|


|..1...2...1..|1...2
|..5..3...1..|5..3
|..X..Y..1..|X..Y

=> (1*3*1) + (2*1*X) + (1*5*Y) - (X*3*1) - (Y*1*1) - (1*5*2)

=> 3 + 2X + 5Y - 3X - Y - 10

=> 2X - 3X + 5Y - Y - 10 + 3

=> - X + 4Y - 7---> eessa equacao de AC na forma geral.

Ponto B
:::::::::::::::

B (2,4)=> Xb = 2 e Yb = 4
- X + 4Y - 7 => a = - 1 ; b = 4 ; c = - 7

dp = h = | aXp + byp + c |
................_____________
......................\|a^2 + b^2


h = | (-1)(2) + (4) (4) + (-7) |
......________________
............\|(-1)^2 + (4)^2


h = | -2 + 16 - 7 |
......__________
...........\| 1 + 16


h = | 14 - 7 |
......______
..........\|17


h =....7
.......___
........\|17


h = 7*\|17
.......______
........\|17*\|17

h = 7*\|17
......_____
..........17

A altura relativa e 7*\|17/17