Question

UFRGS) A distância entre os pontos A (-2, y) e B (6, 7) é 10. O valor de y é: *

A- -1
B-0
C- 1 ou 13
D- -1 e 10

Answer 1

$10=\sqrt{(-2-6)^2+(y-7)^2}\\10=\sqrt{(-8)^2+y^2-14y+49}\\10=\sqrt{64+49+y^2-14y}\\10=\sqrt{y^2-14y+113}\\10^2=y^2-14y+113\\y^2-14y+113-100=0\\y^2-14y+13=0\\\\\frac{-b}{a}=14=13+1\\\\\frac{c}{a}=13=13\cdot1\\\\y=1 ou y=13$