Question

1. a hiker starts at (2, 3) and ends at (6, 7). using the distance formula, how far did the hiker travel?

a. \\(\sqrt{32}\\) units
b. \\(\sqrt{40}\\) units
c. 6 units
d. 8 units

Explanation:

Step1: Recall distance formula

For points $(x_1,y_1)$ and $(x_2,y_2)$, distance $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Step2: Substitute given points

Let $(x_1,y_1)=(2,3)$ and $(x_2,y_2)=(6,7)$.
$d=\sqrt{(6-2)^2+(7-3)^2}$

Step3: Calculate differences

$d=\sqrt{(4)^2+(4)^2}$

Step4: Simplify the expression

$d=\sqrt{16+16}=\sqrt{32}$

Answer:

a. $\sqrt{32}$ units