Question

Determine P(x, y), que divide AB na razão 2, sendo A(1,3) e B(7,9).


alguém que saiba ???????​

Answer 1

Resposta:

A(1,3), B(7,9)

distancia AB

d² = (7 - 1)² + (9 - 3)² = 36 + 36 = 72

d = 6√2

AP = 2PB

AP = 4√2 , PB = 2√2

equação da reta AB

m = (Ay - By)/(Ax - Bx)

m = -6/-6 = 1

y - 3 = 1*(x - 1)

y = x + 2

distancia AP = 4√2 --> d² = 16*2 = 32

d² = (Ax - Px)² + (Ax - Py)²

d² = (1 - x)² + (3 - x - 2)² = 32

d² = x² - 2x + 1 + x² - 2x + 1 = 32

2x² - 4x - 30 =  0

x² - 2x - 15 = 0

delta

d = 4 + 60 = 64

x1 = (2 + 8)/2 = 5

y1 = x1 + 2 = 5 + 2 = 7

P(5,7)

Answer 2

Resposta:

P(5,7)

Explicação passo a passo:

Dividir o segmento AB na razão 2, significa que AP = 2PB

A________________P_________B

$\frac{AP}{PB} =2\\\\\frac{x_P-x_A}{x_B-x_P}=2\\\\\frac{x_P-1}{7-x_P}=2 \\\\x_P-1 =14-2x_P\\\\x_P +2x_P=14+1\\\\3x_P=15\\\\x_P=\frac{15}{3}\\\\x_P=5\\\\\frac{AP}{PB}=2\\\\\frac{y_P-3}{9-y_P} =2\\\\y_P-3=18-2y_P\\\\y_P+2y_P=18+3\\\\3y_P=21\\\\y_P=\frac{21}{3}\\\\y_P=7\\\\P(5,7)$