<p> Taxicab Geometry</p><p>Suppose we define a geometry that lies on a square grid. Think of a city with streets that lie on a square grid and the only paths available are the paths a taxicab might take, such as in the example below:</p><p>To get from the first point to the second point in the diagram above, a taxicab might take the path drawn.</p><p>In taxicab geometry we define the distance between two points as the least number of horizontal and vertical units between the points.</p><p>1. What is the taxicab distance between the two points above? 2. Keeping in mind that taxicabs cannot travel along the diagonal (through buildings): a. Are there any other paths that will give you the same taxicab distance between these two points? _____ b. Outline two more equivalent paths using different colors of pen or pencils. 3. Imagine that you could travel through buildings to get from one point to another. Would the distance be the same? Longer? Shorter? 4. What would you use to calculate that distance? 5. Calculate the diagonal distance for the two points.</p><p>6. What observations can you make about the diagonal (Euclidean) distance compared to the Taxicab distance?</p><p>7. Calculate the Euclidean distance and Taxicab distance for the following two points: (4, 0), (2, 5)</p><p>Taxicab Distance = ______</p><p>Euclidean Distance = ______Name ______Period _____</p><p>Taxicab Geometry</p><p>1. Graph the points listed in the chart below on the coordinate grid. 2. Find the Taxicab distance between each pair of points and record it in the chart. 3. Find the Euclidean distance between each pair of points and record it in the chart. (Show all work.)</p><p>Points to Graph Taxicab Distance Euclidean Distance C(2, 3), D(2, -1) A(-3, -1), E(-1, -2) B(-2, 2), D(2, -1) A(-3, -1), D(2, -1) B(-2, 2), E(-1, -2)</p><p>Show Work for #3 Here</p><p>4. Write a conjecture that describes the relationship between the two points when the Euclidean distance is less than the Taxicab distance.</p><p>5. Write a conjecture that describes the relationship between the two points when the Euclidean distance is equal to the Taxicab Distance.</p>