Question

A lawyer drives from her​ home, located 1 mile east and 8 miles north of the town​ courthouse, to her​ office, located 4 miles west and 4 miles south of the courthouse. Find the distance between the​ lawyer's home and her office.

Answer 1

Answer:

d = 13 miles

Explanation:

Lets say the position of court house is origin in this case

her office is located at 4 miles west and 4 miles south of court house

so here we have coordinate of the office with respect to court house is given as

$r_1 = (-4\hat i - 4\hat j)$

now the position of her home is located at 1 miles east and 8 miles north of the court house

so the coordinates of her home is given as

$r_2 = (1\hat i + 8 \hat j)$

now the change in the position is given as the distance between office and home

$d = r_2 - r_1$

$d = 5 \hat i + 12 \hat j$

$d = \sqrt{5^2 + 12^2} = 13 miles$