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Distance Between Two Points

The content provides an in-depth exploration of calculating distances in the x-y plane, focusing on horizontal, vertical, and diagonal distances, and extends these concepts to understanding circles in the x-y plane.
  • Horizontal and vertical distances can be easily calculated by subtracting the respective coordinates.
  • Diagonal distances require the use of the Pythagorean theorem applied to the slope triangle formed between the two points.
  • Scaling down the slope triangle by the greatest common factor simplifies the calculation of the hypotenuse, which represents the distance between two points.
  • The distance formula is discouraged in favor of a visual and conceptual understanding using the Pythagorean theorem.
  • The equation of a circle in the x-y plane is derived from the Pythagorean theorem, emphasizing the circle's radius as the hypotenuse of slope triangles formed by radii to points on the circle.
Understanding Horizontal and Vertical Distances
Calculating Diagonal Distances
Simplifying Calculations with Proportional Thinking
Circles in the x-y Plane

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