Question

1. on a coordinate grid, your campsite is located at (-4, 10), and the next checkpoint station is located at (-10, -1). each unit in the coordinate plane represents 1.55 miles. find the distance you have to hike to reach the next checkpoint station. a. about 19.4 mi b. about 16.6 mi c. about 25.8 mi d. about 12.5 mi

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $(x_1,y_1)=(-4,10)$ and $(x_2,y_2)=(-10,-1)$.

Step2: Calculate differences

$x_2 - x_1=-10-(-4)=-6$ and $y_2 - y_1=-1 - 10=-11$.

Step3: Square the differences

$(x_2 - x_1)^2=(-6)^2 = 36$ and $(y_2 - y_1)^2=(-11)^2 = 121$.

Step4: Sum the squared differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=36 + 121=157$.

Step5: Take square - root

$d=\sqrt{157}\approx12.53$.

Step6: Adjust for scale

Since each unit represents 1.55 miles, the actual distance $D = 1.55\times12.53\approx19.4$ miles.

Answer:

a. about 19.4 mi