for this activity you will need to design a town with at least four different places, find the distance between each Place using the Pythagorean theorem or the distance formula, choose one row and calculate the distance using the alternative method did you get the same result?

Answer 1

Town Design:

Place 1: Town Hall
Place 2: Park
Place 3: School
Place 4: Supermarket

To calculate the distances between each place, we need to assign coordinates to their locations. Suppose the town is set on a 2-dimensional grid:

Town Hall (TH): (0, 0)
Park (P): (3, 0)
School (S): (0, 4)
Supermarket (SM): (2, 5)

Using these coordinates, we can calculate the distances between the places.

1. Distance between Town Hall and Park (THP):
Using the Pythagorean theorem:
THP = √[(3 - 0)^2 + (0 - 0)^2]
= √(9 + 0)
= √9
= 3 units.

2. Distance between Town Hall and School (THS):
Using the Pythagorean theorem:
THS = √[(0 - 0)^2 + (4 - 0)^2]
= √(0 + 16)
= √16
= 4 units.

3. Distance between Town Hall and Supermarket (THSM):
Using the Pythagorean theorem:
THSM = √[(2 - 0)^2 + (5 - 0)^2]
= √(4 + 25)
= √29 units (approx. 5.39 units).

4. Distance between Park and School (PS):
Using the Pythagorean theorem:
PS = √[(0 - 3)^2 + (4 - 0)^2]
= √(9 + 16)
= √25
= 5 units.

Alternative Method for Row 3 (Town Hall - Supermarket Distance - THSM):

Using the distance formula:
THSM = √[(2 - 0)^2 + (5 - 0)^2]
= √(4 + 25)
= √29 units (approx. 5.39 units).

The results obtained using both the Pythagorean theorem and the distance formula for the Town Hall - Supermarket distance (THSM) are the same.

Answer 2

thanks

Answer 3

You're welcome! If you have any more questions, feel free to ask. Happy designing!