Question

1. a ranger tracks a bear from its den at (-8,-4) to a food source at (6, 10). a) how far did the bear travel?

Explanation:

Step1: Recall distance formula

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

Step2: Identify the points

Here, $(x_1,y_1)=(-8,-4)$ and $(x_2,y_2)=(6,10)$.

Step3: Substitute values into formula

$d=\sqrt{(6 - (-8))^2+(10 - (-4))^2}=\sqrt{(6 + 8)^2+(10 + 4)^2}=\sqrt{14^2+14^2}$.

Step4: Simplify the expression

$d=\sqrt{196 + 196}=\sqrt{392}=\sqrt{196\times2}=14\sqrt{2}$.

Answer:

$14\sqrt{2}$