A lawyer drives from her home, located 3 miles east and 9 miles north of the town courthouse, to her office, located 4 miles west and 15 miles south of the courthouse. Find the distance between the lawyer's home and her office.
The distance between the courthouse and her home has nothing to do with the question.
the distance between here home and her office is
√(15^2 + 4^2) = appr 15.5 miles
If you wanted the distance between the courthouse and her office ....
vector = <3,9> + <-4,-15) = <-1,-6>
distance = √(1+36) = √37 miles
To find the distance between the lawyer's home and her office, we can use the Pythagorean theorem.
Let's break down the problem into two parts: the horizontal distance and the vertical distance.
The horizontal distance traveled by the lawyer can be calculated by subtracting the distance from her home to the courthouse (3 miles) from the distance from her office to the courthouse (4 miles):
Horizontal distance = 4 miles - 3 miles
Horizontal distance = 1 mile
The vertical distance traveled by the lawyer can be calculated by subtracting the distance from her home to the courthouse (9 miles) from the distance from her office to the courthouse (15 miles):
Vertical distance = 15 miles - 9 miles
Vertical distance = 6 miles
Now, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the horizontal distance is one side of the triangle (1 mile), the vertical distance is the other side (6 miles), and the distance between the lawyer's home and office is the hypotenuse that we want to find (let's call it D).
Applying the Pythagorean theorem:
D^2 = (1 mile)^2 + (6 miles)^2
D^2 = 1 mile^2 + 36 miles^2
D^2 = 1 + 36
D^2 = 37
To find D, we need to take the square root of both sides:
D = √37
So, the distance between the lawyer's home and her office is approximately √37 miles.
To find the distance between the lawyer's home and her office, we can use the concept of the Pythagorean theorem.
Step 1: Draw a diagram to visualize the situation. Place the lawyer's home at a location 3 miles east and 9 miles north of the town courthouse. Place her office at a location 4 miles west and 15 miles south of the courthouse.
Step 2: Calculate the total distance traveled east-west. The lawyer travels 3 miles east from her home to the courthouse, and then she travels 4 miles west from the courthouse to her office. The total distance traveled east-west is 3 + 4 = 7 miles.
Step 3: Calculate the total distance traveled north-south. The lawyer travels 9 miles north from her home to the courthouse, and then she travels 15 miles south from the courthouse to her office. The total distance traveled north-south is 9 + 15 = 24 miles.
Step 4: Apply the Pythagorean theorem. In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the total distance traveled east-west is one side, the total distance traveled north-south is the other side, and the distance between the lawyer's home and her office is the hypotenuse. So, we have:
Distance^2 = (east-west distance)^2 + (north-south distance)^2
Distance^2 = 7^2 + 24^2
Distance^2 = 49 + 576
Distance^2 = 625
Step 5: Calculate the square root of 625 to find the distance. The square root of 625 is 25.
Therefore, the distance between the lawyer's home and her office is 25 miles.