Question

Considerando que os pontos D(4, 3), F(x, y) e P(12, –18) são colineares e que P é o ponto médio entre D e F, as coordenadas do ponto F são:

Answer 1

Resposta:

LETRA C (20, -39)

Xd+Xf/2= Xp

4+xf/2= 12

4+xf= 12*2 = 24

xf=24-4

xf= 20

Yd+Yf/2 = Yp

3+yf/2= -18

3+yf= -18*2 = -36

yf= -36 -3

yf= -39

Answer 2

As coordenadas do ponto médio são dadas por:

• $\sf x_P=\dfrac{x_D+x_F}{2}$

• $\sf y_P=\dfrac{y_D+y_F}{2}$

Temos:

• $\sf x_P=\dfrac{x_D+x_F}{2}$

$\sf 12=\dfrac{4+x_F}{2}$

$\sf 4+x_F=2\cdot12$

$\sf 4+x_F=24$

$\sf x_F=24-4$

$\sf \red{x_F=20}$

• $\sf y_P=\dfrac{y_D+y_F}{2}$

$\sf -18=\dfrac{3+y_F}{2}$

$\sf 3+y_F=2\cdot(-18)$

$\sf 3+y_F=-36$

$\sf y_F=-36-3$

$\sf \red{y_F=-39}$

Logo, $\sf \red{F(20,-39)}$