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2017-02-18 02:00

Circle Function Transformation

In collections Geometry Review Expressing Geometric Properties with Equations (GPE) Cluster CCSS High School: Geometry (Circle equations) CCSS High School: Geometry Circle Equations

This example demonstrates the dynamic changes of a circle. Key mathematical concepts include the equation of a circle, piecewise functions, and transformations. Using GeoGebra commands such as Circle, Point, Segment, Intersect, etc., a dynamic geometric figure is constructed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

Circle(A, B) → c
Point(c) → C
Segment(A, C) → g
Intersect(a, f) → D
Segment(A, D) → d
Segment(D, C) → e
Distance(D, C) → distanceDC
Distance(A, D) → distanceAD
Distance(A, C) → distanceAC
Dilate(A, If[0 < h ≤ 1, 1 - h, 0], D) → A'
Segment(A, A') → i
Dilate(D, If[1 < h ≤ 2, 2 - h, 0], C) → D'
Segment(D, D') → j
Angle(C, D, A) → α
Dilate(C, If[2 < h ≤ 3, 3 - h, 0], A) → C'
Segment(C, C') → k
Polygon(A, D, C) → poly1, c_1, a_1, d_1
Distance(A, B) → l
Point(f) → E
Ray(A, E) → m
Point(m) → F
Ray(A, F) → n
Intersect(c, f, 1) → G
Segment(A, G) → q

AI Drawing Prompt Reference

Draw a circle and move a point C on it. Draw a line segment g through points A and C. Find the intersection point D of the circle c and the function f, and draw line segments d and e. Calculate the distances between points D and C, A and D, and A and C. Then, scale point A and D based on the value of h to get point A', and draw line segment i. Similarly, scale point D and C to get point D', and draw line segment j. Calculate the angle CAD, then scale point C to get point C', and draw line segment k. Finally, draw triangle ADC and find the other intersection point G of the circle c and the line f, and draw line segment AG.

The prompt above was compiled from the original drawing commands and is for reference only.