calculate the distance between points (2, 6, 3) and (7, 9, 1).
a. 7.00
b. 7.28
c. 6.16
d. 5.83
a hiker’s current position is at (300m, 500m, 0m) and the peak is at (600m, 900m, 800m). calculate the hiking distance.
a. 965
b. 943
c. 1024
d. 1123

Question

Accepted Answer

# Explanation:
## Step1: Recall the distance formula in 3D
The distance formula between two points $(x_1,y_1,z_1)$ and $(x_2,y_2,z_2)$ is $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2+(z_2 - z_1)^2}$
## Step2: Solve the first problem
For points $(2,6,3)$ and $(7,9,1)$, $x_1 = 2,y_1 = 6,z_1 = 3,x_2 = 7,y_2 = 9,z_2 = 1$
$$
\begin{align*}
d&=\sqrt{(7 - 2)^2+(9 - 6)^2+(1 - 3)^2}\
&=\sqrt{5^2+3^2+(- 2)^2}\
&=\sqrt{25 + 9+4}\
&=\sqrt{38}\approx6.16
\end{align*}
$$
## Step3: Solve the second problem
For points $(300,500,0)$ and $(600,900,800)$, $x_1 = 300,y_1 = 500,z_1 = 0,x_2 = 600,y_2 = 900,z_2 = 800$
$$
\begin{align*}
d&=\sqrt{(600 - 300)^2+(900 - 500)^2+(800 - 0)^2}\
&=\sqrt{300^2+400^2+800^2}\
&=\sqrt{90000+160000+640000}\
&=\sqrt{890000}\approx943
\end{align*}
$$

# Answer:
1. C. 6.16
2. B. 943

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the distance formula in 3D

Step2: Solve the first problem

Step3: Solve the second problem

Answer: