Question bank: Movements and Location: Grid Meshes

In the city of Jardim Feliz, there is a central square with a special design on the ground made of grid meshes. Children play by walking on these meshes, and each square has an exact size. Ana and Pedro agreed to meet at the square, but they want to choose a point on the grid where they can be the same distance from each other. The grid lines represent the city streets, and they can only walk up, down, left, or right, but cannot walk diagonally. Knowing that each little square is 2 meters on each side, how can Ana and Pedro choose a point on the grid of the square where they are 8 meters apart from each other by walking only up, down, left, or right? Draw a simplified map of the grid and indicate the point where Ana and Pedro should meet, considering that they are at different points on the grid.

Imagine you are in a big city and need to help a friend find the central library, which is a very important place. In the city, the streets are organized in a grid pattern, meaning the streets form a large grid with many squares. To get to the library, your friend must walk 5 blocks north and 3 blocks east from a reference point, like the school. Think about the directions your friend should follow and write in which point of the grid he will end up after walking the 5 blocks north and 3 blocks east. Explain why he stops at that specific point.

Rafaela and her father are building a miniature boat together from a grid, where each square of the grid is 5 centimeters long. They decided that the boat will have the shape of a rectangle with 4 squares in width and 8 squares in length. The bottom left corner of the boat is located at point (2,3) on the grid, where the coordinates (x, y) indicate the number of squares to be counted from the origin, towards the right for x and upwards for y, to reach the determined point. Rafaela is tasked with decorating the boat with paper pieces in the shape of a triangle, which will have one vertex at point (2,3) and the hypotenuse parallel to the sides of the boat's rectangle. She must cut the triangles so that the hypotenuse is 10 centimeters long. How many square centimeters of paper will be needed to decorate Rafaela's boat?

Imagine you are a detective in a mysterious city and need to find a hidden treasure. Following the map, you must leave the blue house, walk 5 blocks to the north, 3 to the east, 2 to the south, and 4 to the west to reach the exact location where the treasure is buried. Draw the route you must follow on the gridded map and then write down what the final coordinates of the place where the treasure is hidden are. Remember that each step you take is worth one block of distance in the north, south, east, or west direction.

João and Maria are playing treasure hunt on a large checkered board. João is located at coordinates (2,3) and Maria is at coordinates (5,5). João needs to reach Maria by following a path only through neighboring houses, that is, he can only move to houses to the right, left, above, or below the house where he is. He cannot move diagonally. Describe the path that João must follow to reach Maria, indicating the coordinates of the houses he needs to pass through.