Polygon Area and Transformation Demo by Martin Flashman

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2017-07-24 00:04

In collections Mapping Diagrams: From AB to C&DE, Resource

This example demonstrates the calculation and visualization of polygon area after translation transformation; Core math concepts include polygon area, translation vector, Pythagorean theorem, and bar chart data display; GeoGebra commands/objects used in construction are Point, If, Vector, Sequence, Zip, Textfield, such as implementing translation with Vector, generating point sequences with Sequence, and merging data with Zip; Suitable for high school mathematics teaching, for understanding geometric transformations and area calculations, and also for data visualization education.

GeoGebra Commands & Parameters

Element(f1list, n) → f_1
Element(f2list, n) → f_2
Point(yAxis) → A
If(n ≟ 1, (2, g(y(A))), (2, f(y(A)))) → B
Vector(A, B) → u
Vector(B, C) → v
Vector(A, C) → w
Sequence(k, k, -4, 4, Δx) → xlist
Zip((k, h(k)), k, xlist) → pthlist
Zip(Vector[(0, k), (x(C), h(k))], k, xlist) → vhlist
Zip(Vector[(0, k), (x(B), f_1(k))], k, xlist) → vf1list
Textfield(g) → inputBoxg
Textfield(f) → inputBoxf
Zip(Vector[(x(B), f_1(k)), (x(C), h(k))], k, xlist) → vf2list

AI Drawing Prompt Reference

Draw a coordinate plane with a polygon and its translated copy. Place a point on the y-axis as a reference, then create a translation vector from it to move the polygon. Generate a series of equally spaced points along the x-axis, and from each point draw vertical or horizontal vectors to form a grid-like data display. Include two editable input boxes for adjusting function expressions that control the polygon's shape and area. Finally, show the area change before and after translation using a bar chart or numeric labels, and illustrate the Pythagorean theorem in distance calculations.

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