Question

In Elizabeths town streets run east and west and avenues run north and south each street and avenue is one block apart. if elizabeths house is on 1st street and 4th avenue and her favorite italian restaurant is at 10th street and 16th avenus how many blocks away as the crow flies is the restaurant from Elizabeth?

Answer 1

The correct answer is:

15 blocks.

Explanation:

"As the crow flies" means in a straight line.  This will be a diagonal line connecting the two locations.

Elizabeth's house can be represented by the ordered pair (1, 4), where the x-coordinate represents the street number and the y-coordinate represents the avenue number.  Using this same system, the restaurant is represented by the ordered pair (10, 16).  To find the length of the line segment that would connect the we use the distance formula:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\=\sqrt{(10-1)^2+(16-4)^2} \\=\sqrt{(9)^2+(12)^2} \\=\sqrt{81+144}=\sqrt{225}=15$