Question

A lawyer drives from her​ home, located 2 miles east and 3 miles north of the town​ courthouse, to her​ office, located 5 miles west and 21 miles south of the courthouse. find the distance between the​ lawyer's home and her office. the distance between her home and her office is nothing miles.

Answer 1

The distance between the lawyer's home and her office is approximately 25.20 miles.

Step-by-step explanation:

To find the distance between the lawyer's home and her office, we can use the Pythagorean theorem. The lawyer travels 2 miles east and 3 miles north from her home to the courthouse, so we have a right triangle with legs of length 2 and 3. The length of the hypotenuse, which represents the distance between her home and the courthouse, can be found using the Pythagorean theorem: c^2 = a^2 + b^2.

c^2 = 2^2 + 3^2 = 4 + 9 = 13

c = sqrt(13) ≈ 3.61

The lawyer then drives 5 miles west and 21 miles south from the courthouse to her office, forming another right triangle with legs of length 5 and 21. The length of the hypotenuse, which represents the distance between the courthouse and her office, can be found using the same process: c^2 = 5^2 + 21^2.

c^2 = 25 + 441 = 466

c = sqrt(466) ≈ 21.59

To find the distance between her home and her office, we need to add the lengths of the two hypotenuses: 3.61 + 21.59 ≈ 25.20 miles.

Answer 2

Let the town​ courthouse be the origin of coordinate plane, the positive direction of x-axis is west and negative direction is east, the positive direction of y-axis is north and negative direction is south. Then a lawyer home has coordinates (-2,3) and lawyer office has coordinates (5, -21).

Use the distance formula
`d= √((x_1-x_2)^2+(y_1-y_2)^2)` to get the distance between lawyer's home and office:


`d=√((x_1-x_2)^2+(y_1-y_2)^2)=√((-2-5)^2+(3-(-21))^2)=`

`=√(7^2+24^2) = √(49+576) = √(625) =25`.
Answer: 25 miles.