Question

question 11 of 13, step 1 of 1
your itinerary contains a grid map of sydney, with each unit on the grid representing 0.5 kilometers. if the sydney opera house is located at (-3, -3) and the queen victoria building is located at (4, -3), 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: 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, $x_1=-3,y_1 = - 3,x_2 = 4,y_2=-3$.

Step2: Substitute values

Substitute the values into the formula: $d=\sqrt{(4-(-3))^2+((-3)-(-3))^2}=\sqrt{(4 + 3)^2+( - 3+3)^2}=\sqrt{7^2+0^2}=\sqrt{49}=7$.

Step3: Adjust for scale

Since each unit on the grid represents $0.5$ kilometers, the actual distance $D=7\times0.5 = 3.50$ kilometers.

Answer:

$3.50$