Question

the coordinates on a map for city a are (53, 13) and those for city b are (118, 72). note that coordinates represent miles. find the distance between the cities to the nearest mile.

Explanation:

Step1: Identify 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, $(x_1,y_1)=(53,13)$ and $(x_2,y_2)=(118,72)$.

Step2: Calculate differences

$x_2 - x_1=118 - 53 = 65$ and $y_2 - y_1=72 - 13 = 59$.

Step3: Square the differences

$(x_2 - x_1)^2=65^2 = 4225$ and $(y_2 - y_1)^2=59^2 = 3481$.

Step4: Sum the squared - differences

$4225+3481 = 7706$.

Step5: Calculate the square - root

$d=\sqrt{7706}\approx88$.

Answer:

88