Question

um extremo de um segmento é o ponto R (7, 5). sendo M(3/2, -1) o ponto médio desse segmento, as coordenadas do outro extremo é o ponto ​

Answer 1

$Seja~ (x_m,y_m)~ o~ ponto ~medio ~de ~um ~segmeneto~AB,~temos:\\\\Ponto~medio~\left(x_m~,~y_m\right)~=~\left(\frac{x_A+x_B}{2}~,~\frac{y_A+y_B}{2}\right)\\\\Substituindo~os~valores~do~enunciado:\\\\\\\left(\frac{3}{2}~,~-1\right)~=~\left(\frac{7+x_B}{2}~,~\frac{5+y_B}{2}\right)\\\\\\\rightarrow~\frac{3}{2}~=~\frac{7+x_B}{2}\\\\\rightarrow~-1~=~\frac{5+y_B}{2}$

Resolvendo as duas equações, temos:

$\rightarrow~\frac{3}{2}~=~\frac{7+x_B}{2}\\\\7+x_B=2~.~\frac{3}{2}\\\\x_B=3-7\\\\\boxed{x_B=-4}\\\\\rightarrow~-1~=~\frac{5+y_B}{2}\\\\5+y_B=2~.~-1\\\\y_B=-2-5\\\\\boxed{y_B=-7}$

A outra extremidade será, portanto:

B = (-4 , -7)

Answer 2

Resposta:

d) (− 4, − 7).

Alternativas:

a) (4, 7).  

b) (2, 3).  

c) (7, 4).

d) (− 4, − 7).  

e) (− 2, − 3).

Explicação passo-a-passo:

(geekie)

$M\left(\frac{3}{2},-1\right)$

$x+\frac{7}{2}=\frac{3}{2}\therefore x=-4$

$\frac{y+5}{2}=-1\therefore y=-7$

Logo, $\left(x,\:y\right)=\left(-4,\:-7\right)$