Looking for Pythagoras- Math Reflection Quesions Investigation 1

1. In the city of Euclid, how does the driving distance from one place to another compare to the flying distance?

          In most cases, the driving distance from one place to another is longer than the flying distance. When driving you have to drive on roads and you can't cut between land to take short cuts. But, when flying you can fly diagonally cutting across land and not following roads. In other cases the driving distance from one place to another compared to the flying distance are the same. This happens when there is one straight route where not matter what flying or driving, there is no difference in distance. Overall, the flying distance can never be more than the driving distance, it's either less than or equal to the driving distance. 

2. Suppose you know the coordinates of two landmarks in Euclid. How can you find the distance between those two landmarks?
          To find the distance between the coordinates of two landmarks in Euclid, you can subtract x1 from x2, and also subtract y1 from y2. Then you take the absolutes value of x1-x2 and y1-y2. Lastly, you add the two absolute values, which gets you to the distance between the coordinates of two landmarks in Euclid. 

3. What are some strategies for finding areas of figures drawn on a grid?

          There are a couple strategies for finding areas of figures drawn on a grid: 

                    1. If it's a regular shape with "full boxes" you can just count the boxes that make up the area of the figure on the grid. 

                    2. It it's an irregular shape, then you can deconstruct the shape into rectangles and triangles. Then calculate the area of each rectangle or triangle. Lastly, add all the areas of the deconstructed shape together and you have your answer.  

                    3. Enclose the figure on the grid in a larger rectangle/square. Then find out how much the area of the unwanted parts of the larger rectangle/square is. Lastly, subtract the areas of the unwanted parts from the area of the larger rectangle/square.