A lawyer drives from her​ home, located 8 miles east and 17 miles north of the town​ courthouse, to her​ office, located 2 miles west and 7 miles south of the courthouse. Find the distance between the​ lawyer's home and her office.
If the town courthouse is (0,0), her home would be at (8,17)
her office at (-2,-7)
use the "distance formula between two points" to find the distance.
marco spends a total of d dollars on postage to mil party invitations to each of g gusts
d = -8 - 17i - 2 - 7i = -10 - 24i .
d = sqrt(10^2+24^2) =
To find the distance between the lawyer's home and office, we can use the Pythagorean theorem.
First, let's visualize the situation by drawing a grid. Place the courthouse at the origin (0,0). The lawyer's home is located at (8, 17) since it is 8 miles east and 17 miles north of the courthouse. The office is located at (-2, -7) since it is 2 miles west and 7 miles south of the courthouse.
Now, we can find the distance between the points (8, 17) and (-2, -7) using the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
The horizontal distance between the two points is the difference between their x-coordinates: 8 - (-2) = 10.
The vertical distance between the two points is the difference between their y-coordinates: 17 - (-7) = 24.
Using these values, we can apply the Pythagorean theorem:
Distance^2 = (horizontal distance)^2 + (vertical distance)^2
Distance^2 = 10^2 + 24^2
Distance^2 = 100 + 576
Distance^2 = 676
Taking the square root of both sides, we find:
Distance = sqrt(676) = 26
So, the distance between the lawyer's home and office is 26 miles.