Question

6 joan lost his backpack, but because it had an air - tag, he was able to use cloud to locate it. the system was able to represent joans location at (5, 3) and said the backpack was 10 miles away at the point (11, y). the system lost connection before y could be calculated. use the distance formula to help joan locate his backpack.
a y = 3
b y = - 2
c y = - 5
d y = 5
e y = 11
f y = - 11

Explanation:

Step1: Escribir la fórmula de la distancia

La fórmula de la distancia entre dos puntos \((x_1,y_1)\) y \((x_2,y_2)\) es \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Aquí, \(d = 10\), \(x_1=5\), \(y_1 = 3\), \(x_2=11\), \(y_2=y\). Sustituyendo: \(10=\sqrt{(11 - 5)^2+(y - 3)^2}\)

Step2: Simplificar la ecuación

Primero, calcula \((11 - 5)^2=6^2 = 36\). La ecuación se convierte en \(10=\sqrt{36+(y - 3)^2}\). Elevando al cuadrado ambos lados: \(100=36+(y - 3)^2\). Luego, restar 36: \((y - 3)^2=100 - 36=64\)

Step3: Resolver para \(y\)

Tomar la raíz cuadrada: \(y - 3=\pm8\). Si \(y - 3 = 8\), entonces \(y=8 + 3=11\). Si \(y - 3=-8\), entonces \(y=-8 + 3=-5\)

Answer:

C. \(y=-5\), E. \(y = 11\)