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.
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
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.
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.
thank you
Oh, lawyer jokes. They always make me plead for more! Let's calculate the distance between the lawyer's home and her office, step by step, using the distance formula.
First, we need to find the horizontal (east-west) distance between the home and the office. From the home, she drives 6 miles east, and then goes 4 miles west to her office. So the horizontal distance is 6 miles + 4 miles = 10 miles.
Next, we calculate the vertical (north-south) distance. From the home, she goes 10 miles north, and then 14 miles south to her office. The vertical distance is 10 miles + 14 miles = 24 miles.
Finally, to find the total distance, we can use the Pythagorean theorem. The distance between the home and office is equal to the square root of the sum of the squares of the horizontal and vertical distances.
Distance = sqrt((10 miles)^2 + (24 miles)^2)
Distance = sqrt(100 miles^2 + 576 miles^2)
Distance = sqrt(67600 miles^2)
Distance ≈ 260 miles.
So, it looks like the distance between the lawyer's home and office is approximately 260 miles, rather than 26 miles. Oops, looks like someone's been telling lawyer jokes and math jokes all in one!
To find the distance between the lawyer's home and her office, you can use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, we can consider the lawyer's home and office as two points on a coordinate plane. Let's assume the lawyer's home is at point A and her office is at point B.
The distance traveled in the east-west direction is 6 miles (distance between home and courthouse) - 4 miles (distance between office and courthouse) = 2 miles west.
The distance traveled in the north-south direction is 10 miles (home to courthouse) - 14 miles (office to courthouse) = 4 miles south.
Now, we have a right-angled triangle with two sides measuring 2 miles and 4 miles. We can use the Pythagorean theorem to find the length of the hypotenuse, which represents the distance between the lawyer's home and her office.
Applying the theorem:
Hypotenuse^2 = 2^2 + 4^2
Hypotenuse^2 = 4 + 16
Hypotenuse^2 = 20
Taking the square root of both sides:
Hypotenuse = √20
Simplifying the square root of 20, we get:
Hypotenuse ≈ 4.47
Thus, the distance between the lawyer's home and her office is approximately 4.47 miles, which rounded to the nearest whole number is 4 miles.
However, it seems that the answer provided to you is 26 miles. This suggests that there might be additional information or steps that have not been provided. Without further information or clarification, it is difficult to determine how the answer of 26 miles was derived.
yes, you do
(-4-6)^2 + (-14-10)^2 = 10^2+24^2 = 26^2