42. Tim lives on Taylor Avenue, $1400 \mathrm{~m}$ west of the intersection with Swift Street. The library is on Swift Street, $1050 \mathrm{~m}$ north of the intersection with Taylor Avenue.

Step 1 ：Let west_distance be the distance Tim lives west of the intersection, and north_distance be the distance the library is north of the intersection. We have west_distance = 1400 m and north_distance = 1050 m.

Step 2 ：Use the Pythagorean theorem to find the distance between Tim's house and the library: \(distance = \sqrt{west\_distance^2 + north\_distance^2}\)

Step 3 ：Substitute the values: \(distance = \sqrt{1400^2 + 1050^2}\)

Step 4 ：Calculate the distance: \(distance = 1750\)

Step 5 ：\(\boxed{The distance between Tim's house and the library is 1750 meters.}\)