Point Distance on the Cartesian Coordinate Plane

Distance Between Two Points on the Cartesian Coordinate Plane Take a look at the two points on the Cartesian Coordinate Plane. They are called "A" and "B" and their values are determined by the four sliders you see. Use these sliders to answer the questions that follow. Feel free to adjust the sliders that you see on the screen (the bars with the dots on them) to play around with the different points. Make sure you pay close attention to which point is A and which is B.
  1. With the sliders in their starting configuration, try to determine the distance between A and B. Explain why your answer is correct.
  2. Adjust the value of the sliders so that the x values of A and B are the same. Use the text above the sliders to help. What is the distance between A and B now? Explain why your answer is correct.
  3. For the following questions, set the sliders so that A and B have the following coordinates. As you do, take a look at the squares that form. The area of the squares (what you can fit inside of each square) appears in the small text underneath A, B, and C.
    1. A=(0,3), B=(4,6)
    2. A=(-2,0), B=(6,6)
    3. Choose any point for A and B that you want (other than the two above)
    4. What do you notice? Can you say anything about how to find the distance between two points on the coordinate plane?