A Lawyer's Distance Dilemma

The Distance Dilemma

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:

d = 13 miles Explanation: Let's say the position of the courthouse is the origin in this case. Her office is located at 4 miles west and 4 miles south of the courthouse. Therefore, the coordinates of the office with respect to the courthouse can be given as: r1 = (-4i - 4j) Now, the position of her home is located at 1 mile east and 8 miles north of the courthouse. So, the coordinates of her home can be given as: r2 = (1i + 8j) The change in the position is given as the distance between the office and home: d = r2 - r1 d = 5i + 12j d = √(5^2 + 12^2) = 13 miles

Final answer:

The distance between the lawyer's home and her office, given their respective geographical positions relative to the courthouse and using the Pythagorean theorem, is 13 miles. Explanation: From the information presented, we can determine the positions of the lawyer's home and office relative to the courthouse. The lawyer's home is 1 mile east and 8 miles north of the courthouse. The office is 4 miles west and 4 miles south of the courthouse. Therefore, in total, the office is 5 miles west and 12 miles south of the home. By applying the Pythagorean theorem, we can find the direct distance between the lawyer's home and her office to be 13 miles.

How does the Pythagorean theorem help in finding the distance between two points located at different positions relative to a reference point?

The Pythagorean theorem is a useful tool in calculating the direct distance between two points located at different positions relative to a reference point. By treating the positions as coordinates and forming a right-angled triangle, the theorem helps in determining the hypotenuse, which represents the direct distance between the two points. In the case of the lawyer's home and office scenario, the Pythagorean theorem was applied to find the distance between the two points based on their respective positions relative to the courthouse. By using the theorem's formula and the given coordinates, the distance of 13 miles was calculated effectively.
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