Question

the library is 4 blocks north and 9 blocks east of the school. The museum is 9 blocks east and 11 blocks south of the school. How far is it from the library to the museum?

Answer 1

Summary: Solve
`√(90)`
Starting at (0,0), the school's location, at least for the definition I will use, you add 4 to the y value (0,4), 9 blocks east, so you add 9 to the x value (9,4), and there is the library's location. Adding 9 to the x value and subtracting 11 from 4 you get (18,-7). You'll need the distance formula for the rest, which is:
`\sqrt({ x_(1) - x_(2))^2 + ({y_(1) - y_(2))^2`. So, plugging in the numbers, the first x becomes 9, and the second one becomes 18, so the first portion of the equation is (9-18)^2. As for the second part of the equation, you plug 4 into the first y, and -7 into the second "y", ending up with (4-7)^2. So, the equation now becomes
`√((9-18)^2 + (4-7)^2)`. Using that, (-9)^2 is 81, and (-3)^2 is 9, so 81+9 is 90, and now, for the final portion of the equation, you find the square root of 90, which is about 9.49. So, the distance between the library and museum is about 9.49 (or 9.5) blocks.