A Distance Problem: Lawyer's Home and Office

Calculating the Distance

A lawyer drives from her home, located 88 miles east and 18 miles north of the town courthouse, to her office, located 13 miles west and 54 miles south of the courthouse. To find the distance between the lawyer's home and her office, we can use the distance formula in a 2D coordinate plane.

Answer

The distance between the lawyer's home and her office is 124 miles.

Explanation: Given information: first, let's assume that:

• x-axis (west = positive, east = negative)
• y-axis (north = positive, south = negative)

Thus, the coordinates of the lawyer's home are (-88, 18) and the coordinates of the office are (13, -54). To calculate the distance between the lawyer's home and her office, we use the formula:

R = √(x₂ - x₁)² + (y₂ - y₁)²
     = √(13 - (-88))² + (-54 - 18)²
     = 124 miles

What are the coordinates of the lawyer's home and office in relation to the town courthouse?

The lawyer's home is located 88 miles east and 18 miles north of the town courthouse, while her office is located 13 miles west and 54 miles south of the courthouse.