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.
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 [tex]d= \sqrt{(x_1-x_2)^2+(y_1-y_2)^2} [/tex] to get the distance between lawyer's home and office: [tex]d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}=\sqrt{(-2-5)^2+(3-(-21))^2}=[/tex] [tex]=\sqrt{7^2+24^2} = \sqrt{49+576} = \sqrt{625} =25[/tex]. Answer: 25 miles.
