Question

A lawyer drives from her home, located 6 miles east and 10 miles north of the town courthouse, to her office, located 4 miles west and 14 miles south of the courthouse. Find the distance between the lawyer's home and her office.

I know the answer is 26 miles but I cannot figure out how they came up with that answer using the distance formula.

Thank you.

Answer 1

It looks like you need to find the shortest distance (as the crow flies) between the home and the office.

Use the Pythagorean Theorem.

6^2 + 10^2 = c^2
136 = c^2
11.67 = c

4^2 + 14^2 = c^2
212 = c^2
14.56 = c

11.67 + 14.56 = 26.2 = 26 miles

Answer 2

The result above is the length of the path from home to courthouse and then on to office.

the distance z from home:(6,10) to office:(-4,-14) is

This is just a scaled-up 5-12-13 triangle, being 10-24-26.

Answer 3

Steve,

I'm not sure what you mean by a "scaled-up" triangle. And where did you get the 10-24-26?

Also, if you use those coordinates and the distance formula, you don't get 26 miles.

Answer 4

yes, you do

(-4-6)^2 + (-14-10)^2 = 10^2+24^2 = 26^2

Answer 5

thank you