Question

A lawyer drives from her​ home, located 2 miles east and 3 miles north of the town​ courthouse, to her​ office, located 5 miles west and 21 miles south of the courthouse. find the distance between the​ lawyer's home and her office. the distance between her home and her office is nothing miles.

Answer 1

Let the town​ courthouse be the origin of coordinate plane, the positive direction of x-axis is west and negative direction is east, the positive direction of y-axis is north and negative direction is south. Then a lawyer home has coordinates (-2,3) and lawyer office has coordinates (5, -21).

Use the distance formula $d= \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$ to get the distance between lawyer's home and office:

$d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}=\sqrt{(-2-5)^2+(3-(-21))^2}=$
$=\sqrt{7^2+24^2} = \sqrt{49+576} = \sqrt{625} =25$.
Answer: 25 miles.