Question

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

a. 8 units
b. $sqrt{40}$ units
c. $sqrt{32}$ units
d. 6 units

Explanation:

Step1: Identify 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, $(x_1,y_1)=(2,3)$ and $(x_2,y_2)=(6,7)$.

Step2: Substitute values

Substitute $x_1 = 2$, $y_1 = 3$, $x_2 = 6$, and $y_2 = 7$ into the formula: $d=\sqrt{(6 - 2)^2+(7 - 3)^2}=\sqrt{4^2+4^2}=\sqrt{16 + 16}=\sqrt{32}$.

Answer:

C. $\sqrt{32}$ units