# A doctor drives from her home , located 3 miles east and 4 miles north of town to her office, located 3 miles west and 4 miles south of the courthouse. Therefore what would be the distance between...

A doctor drives from her home , located 3 miles east and 4 miles north of town to her office, located 3 miles west and 4 miles south of the courthouse. Therefore what would be the distance between the doctor's home and office?

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A doctor drives from her home ,located 3 miles east and 4 miles north of town to her office, located 3 miles west and 4 miles south of the courthouse. It is assumed that the courthouse is the center of the the town.

The distance of the doctor's home and the courthouse is `sqrt(4^2 + 3^2)` = 5 miles. Similarly, the distance of the office from the courthouse to the office is also 5 miles. If the line joining the doctor's home to the courthouse is extended it reaches the office.

This gives the distance between the doctor's home and office as 10 miles.

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The home and the courthouse form a triangle as do the courthouse and the office. These triangles are both 3,4,5 triangles, and the sides of the triangles that make a straight line from the doctor's home and office are both 5 miles each.

You can find this by using the Pythagorean Theorem:

`sqrt(A^2 + B^2)=C^2` where A=3, B=4, and thus C=5

Adding the two hypotenuses gives you 10 miles,

Therefore the total distance is 10 miles.