Question

On a coordinate grid, your campsite is located at (2,-10) and the next checkpoint station is located at (0,-3). Each unit in the coordinate plane represents 1.4 miles. Find the distance you have to hike to reach the next checkpoint station.

Answer 1

Location of Campsite = (2, -10)

Location of Checkpoint Station = (0, -3)

.$\begin {aligned} \therefore \end {aligned}$ x₁ = 2 ; y₁ = -10

x₂ = 0 ; y₂ = -3

1 unit = 1.4miles

let, the distance between campsite and checkpoint station = r

from, distance between 2 points = $\begin {aligned} \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \end {aligned}$

r = $\begin {aligned} \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \end {aligned}$

r = $\begin {aligned} \sqrt{(0-2)^2+(-3-(-10))^2} \end {aligned}$

r = $\begin {aligned} \sqrt{(-2)^2+(-3+10)^2} \end {aligned}$

r = $\begin {aligned} \sqrt{4+(-7)^2} \end {aligned}$

r = $\begin {aligned} \sqrt{4+49} \end {aligned}$

r = $\begin {aligned} \sqrt{53} \end {aligned}$

r = 7.28 units

$\begin {aligned} \therefore \end {aligned}$ the distance between campsite and checkpoint station = 7.28 units

However since 1 unit = 1.4 miles,

7.28 units = 1.4 $\begin {aligned} \times \end {aligned}$ 7.28 = 10.192 miles

$\begin {aligned} \therefore \end {aligned}$ the distance between campsite and checkpoint station = 10.192 miles