Question

your backpackers guide contains a grid map of london, with each unit on the grid representing 0.125 kilometers. if trafalgar square is located at (-2, -5) and westminster abbey is located at (-2, 5), what is the direct distance (not walking distance, which would have to account for bridges and roadways) between the two landmarks in kilometers? round your answer to two decimal places, if necessary.

Explanation:

Step1: Identify the distance formula for two - points in a coordinate plane

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, $x_1=-2,y_1 = - 5,x_2=-2,y_2 = 5$.

Step2: Substitute the values into the formula

Since $x_1=x_2=-2$, the formula simplifies to $d=\sqrt{(-2+2)^2+(5 + 5)^2}=\sqrt{0+(10)^2}=\sqrt{100}=10$ (in grid - units).

Step3: Convert grid - units to kilometers

Each grid - unit represents $0.125$ kilometers. So the distance in kilometers is $d_{km}=10\times0.125 = 1.25$ kilometers.

Answer:

$1.25$