Question

Dadas as coordenadas do ponto médio M= (2,5), quais são as coordenadas de extremidade A do segmento de reta que a outra extremidade está no B= (5,5)?

A) M= (-1,5)
B) M= (-1,1)
C) M= (1,5)
D) M= (1,-5)
E) M= (5,-1)

Answer 1

$A(x_{A},y_{A})$

$x_{M}=\dfrac{x_{A}+x_{B}}{2}\\2=\dfrac{x_{A}+5}{2}\\x_{A}+5=4\\x_{A}=4-5=-1$

$y_{M}=\dfrac{y_{A}+y_{B}}{2}\\5=\dfrac{y_{A}+5}{2}\\y_{A}+5=10\\y_{A}=10-5=5$

$A(-1,5)$