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.
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.
Answers
Ms. Sue
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
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
Steve
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.
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.
Carly
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.
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.
Steve
yes, you do
(-4-6)^2 + (-14-10)^2 = 10^2+24^2 = 26^2
(-4-6)^2 + (-14-10)^2 = 10^2+24^2 = 26^2
carly
thank you