GEUP
Explore geometry and create interactive and
dynamic math calculations and visualizations
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Documentation - Geometric transformations

Table of contents

4.1 Translated point given number

Create a point that is obtained moving a point on a path a given distance.

To create:
1º Detect and click on the point to translate.
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Select the path:
On a line:
(case a) Detect and click on a 2º point: [the first point will be translated on the ray(imaginary) through both points].
(case b) If the first point is an endpoint of a ray, detect and click on the ray: [the first point will be translated on the ray].
(case c) If the first point is the origin of an axis, detect and click on the axis: [the first point will be translated on the axis].

On a circle: The point to move should belong to the circle.Detect and click on the circle: [the first point will be tranlated on the circle].
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3º Detect and click on the number that defines the distance to translate the first point.



4.2 Symmetry

Create the symmetrical image of an element across a point (simmetry center).

To create:
1º Detect and click on the element to transform (point, segment, line, ray, circle, arc or polygon).
2º Detect and click on a point (simmetry center).



4.3 Reflection

Create the image of an element reflected across a simmetry axis.

To create:
1º Detect and click on the element to transform (point, segment, line, ray, circle, arc or polygon).
2º Detect and click on the simmetry axis (segment, line, ray, axis or side of a polygon).



4.4 Translation

Create the image of an element translated by a given vector.

To create:
1º Detect and click on the element to transform (point, segment, line, ray, circle, arc or polygon).
2º Detect and click on two points that defines the vector.



4.5 Rotation

Create the image of an element rotated around a point a given angular value.

To create:
1º Detect and click on the element to transform (point, segment, line, ray, circle, arc o polygon).
2º Detect and click on a point(rotation center).
3º Detect and click on a number (angular value).



4.6 Dilation

Create the image of an element dilated from a point by a given factor.

To create:
1º Detect and click on the element to transform (point, segment, line, ray, circle, arc or polygon).
2º Detect and click on a point (dilation center).
3º Detect and click on a number (factor).



4.7 Inversion

Create the inverse point(P') of a given point(P), given a circle(radius = r). The center of the circle is the inversion center (O). OP x OP' = r²

To create: Detect and click on the point to transform and on the circle.


Table of contents
 
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