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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justaguide's profile pic

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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.

zach2794's profile pic

Posted on

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.

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