How can I calculate the distance between two points on a coordinate plane?

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To find the distance between two points on a coordinate plane, you can use the Distance Formula. This formula is derived from the Pythagorean Theorem and is an essential tool in coordinate geometry.

The Distance Formula is expressed as:

d = √(x2 – x1)2 + (y2 – y1)2

Where:

  • d = distance between the two points
  • (x1, y1) = coordinates of the first point
  • (x2, y2) = coordinates of the second point

Here’s a step-by-step guide on how to use the Distance Formula:

  1. Identify the coordinates of the two points. For example, consider Point A at (2, 3) and Point B at (5, 7).
  2. Substitute the coordinates into the formula. Using our example:

    3. d = √((5 – 2)2 + (7 – 3)2)

  3. Simplify the expressions within the parentheses:

    4. d = √((3)2 + (4)2)

  4. Calculate the squares:

    5. d = √(9 + 16)

  5. Add the results:

    6. d = √(25)

  6. Take the square root:

    7. d = 5

So, the distance between Point A (2, 3) and Point B (5, 7) is 5 units.

This method can be applied to any pair of points on a coordinate plane, making it a versatile tool for various mathematical and real-world applications.

Whether you’re solving problems in geometry, physics, or computer science, mastering the Distance Formula will enhance your understanding of how points relate to each other in space!

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