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Find Endpoint of a Segment Given Midpoint & Other Endpoint

Find Endpoint of a Segment Given Midpoint & Other Endpoint
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2015-10-05 08:54
VectorCoordinate GeometryGeometric Construction
In collections Expressing Geometric Properties with Equations (GPE) Cluster
This applet provides students with the opportunity to algebraically determine the coordinates of the endpoint of a segment given the coordinates of the midpoint and another endpoint. Key mathematical concepts include coordinate geometry and vectors. The construction uses commands such as Sequence, Segment, Midpoint, and Textfield. Suitable for students in middle school and above for geometric construction.

GeoGebra Commands & Parameters

  1. Sequence(i, i, -20, 20, 1) → list1
  2. Sequence(i, i, -10, 10, 1) → list2
  3. Segment(A, B) → a
  4. Midpoint(A, B) → M
  5. Textfield(b) → InputBox1
  6. Textfield(c) → InputBox2
  7. Midpoint(a) → C
  8. Segment(A, C) → d
  9. Segment(C, B) → e

AI Drawing Prompt Reference

Draw a segment AB with a known midpoint M and one endpoint A. Use input fields to determine the coordinates of the other endpoint B. First, create two sequences of integers from -20 to 20 and -10 to 10, and use these as possible coordinates for points A and B. Then, draw segment AB, find its midpoint M, and input the coordinates of B. Based on the input, calculate a new midpoint C, and draw segments AC and CB.
The prompt above was compiled from the original drawing commands and is for reference only.