Question

Plot a point in Quadrant II and one in Quadrant IV. Find a path between the two points and calculate its (taxi cab) distance. Can you think of a formula (in terms of coordinates) for distance in the taxicab geometry? Justify your answers.

Answer 1

To plot a point in Quadrant II, choose a negative x-coordinate and a positive y-coordinate. To plot a point in Quadrant IV, choose a positive x-coordinate and a negative y-coordinate. The taxi cab distance can be calculated using the formula Distance = |x1 - x2| + |y1 - y2|.

Step-by-step explanation:

To plot a point in Quadrant II, we need to choose a negative x-coordinate and a positive y-coordinate. For example, (-3, 5) is a point in Quadrant II. To plot a point in Quadrant IV, we need to choose a positive x-coordinate and a negative y-coordinate. For example, (2, -4) is a point in Quadrant IV.

To find the taxi cab distance between these two points, we can use the formula:
Distance = |x1 - x2| + |y1 - y2|

For our example, the coordinates of the two points are (-3, 5) and (2, -4), so the taxi cab distance would be |(-3) - 2| + |5 - (-4)| = 5 + 9 = 14.