Question

a hiker wants to travel directly from a point at (2, 1) to (8, 5). what is the straight - line distance the hiker will travel?
a. 5 units
b. \\( \sqrt{61} \\) units
c. 7 units
d. \\( \sqrt{52} \\) units

Explanation:

Step1: Use the distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $(x_1,y_1)=(2,1)$ and $(x_2,y_2)=(8,5)$.

Step2: Substitute the values

Substitute $x_1 = 2,y_1 = 1,x_2 = 8,y_2 = 5$ into the formula: $d=\sqrt{(8 - 2)^2+(5 - 1)^2}$.

Step3: Calculate the squares

First, calculate $(8 - 2)^2=6^2 = 36$ and $(5 - 1)^2=4^2 = 16$.

Step4: Add and take square - root

Then, $d=\sqrt{36 + 16}=\sqrt{52}$.

Answer:

d. $\sqrt{52}$ units