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Closest Point 2

Closest Point 2
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2019-11-18 10:08
VectorTrigonometryCoordinate GeometryOptimizationGeometric Construction
In collections Exploring Orthogonality
This example demonstrates the problem of finding the closest point from a point to a line or curve in a 2D plane. Core mathematical concepts involved include distance formula, Pythagorean theorem, and vector projection. Construction highlights the use of GeoGebra commands and objects such as Line, Point, Segment, OrthogonalLine, Intersect, and Angle. Suitable for high school students and teachers learning analytical geometry and vector mathematics.

GeoGebra Commands & Parameters

  1. Line(A, B) → f
  2. Point(f) → w
  3. Segment(x_0, w) → g
  4. OrthogonalLine(x_0, f) → h
  5. Intersect(f, h) → w_0
  6. Segment(x_0, w_0) → i
  7. Angle(x_0, w_0, A) → α

AI Drawing Prompt Reference

Draw a line AB, then select a point w on the line. Draw a segment from point x_0 to point w, and draw a line h perpendicular to line AB from x_0. The intersection of h and AB is point w_0, which is the closest point from x_0 to line AB. Finally, draw a segment from x_0 to w_0 and measure the angle α formed by x_0, w_0, and point A.
The prompt above was compiled from the original drawing commands and is for reference only.