# Dynamic Geometry tab

## Menu of the Dynamic Geometry Tab

### Actions

This menu groups the different possible actions on the drawing zone and on theirs objects.

Copy the drawing

Copies the drawing zone into the Clipboard

Insert the drawing into the NotePad

Copies the drawing zone into  casyopee's NotePad..

Hide/show grid

There is a grid on the drawing zone, helping to create points with simple coordinates. This grid can be visible or hidden.

Center Axis

Centers the origin of the coordinate system in the drawing zone.

Stop  mobile points
Points are mobile when they a have a non zero velocity, or depend on a point or a parameter with a non zero velocity. This entry is a switch allowing to stop or run again all these points.

Detach geometry tab
This entry is a switch allowing  to display the dynamic geometry tab in a separate window, and to come back to the staandard organisation in which the  dynamic geometry tab covers the algebra tab.
Display the hidden objects

After activting this entry all objects in the drawing zone will be visible..

Redraw All

This entry redraws the drawing zone. One should use this when the display seems uncorrect.

Relationship between objects

This menu allows to know if a point belongs to a line, to a circle or to a curve. Its allows also to verify the equality between objects. One has to click on the first and then on the second object.

### Create

This menu groups the objects that  can be created in Dynamic Geometry.

Note Under the menu, a toolbar proposes different buttons which allow to reach more rapidly the given functions in the menus. As the icons are consistent, there is not a detailed description for the buttons.

#### Point

This menu groups the numerous available manners to create a point.

##### Coordinate Point

An entry form opens, that allows to enter a formula for the each coordinate X and Y. Alternatively a complex formula can be entered.

##### Fixed or Free Point or Intersection

After choosing the menu, just click at any place in the drawing zone.

Note

1. A fixed point is always proposed. If the mouse is near a point on the grid, this point is proposed. If the mouse is near an object (line, circle, curve), a free point on this object is proposed also proposed. If it is near two objects whose intersection can be calculated, an intersection point is proposed. In other cases, a free point on the plan is proposed.

2. These points can also be created on the fly when creating other objects.

##### MidPoint

After choosing a segment or two points, this menu allows to create a point at the middle of this segment.

##### Reported Point

This menu allows to create a reported point related to another point of a certain distance, alongside of a certain vector. It's necessary to choose five points: the mentioned point, two points defining the direction of the transfer, and finally two points defining the distance.

##### Reported  Point Algebraic

This menu allows to create a reported point related to another point of a certain algebraic distance, alongside of a certain vector. It's necessary to choose three points: the first mentioned point, two points defining the vector direction; and enter an algebraic expression defining the distance.

#### Line

This menu groups different and available manners to create a straight line.

##### Segment

After choosing two points, this menu allows to create a segment linking these two points.

##### Line by two Points

After choosing two points, this menu allows to create a line passing through these two points.

##### Parallel Line

After choosing a point and a line (line, half-line, segment), this menu allows to create a line parallel to the chosen line and passing through the chosen point.

##### Perpendicular Line

After choosing a point and a line (line, half-line, segment), this menu allows to create a line perpendicular to the chosen line, passing through the chosen point.

##### Tangent Line

It is necessary that the derivative of the function defining the curve has been created by calculation in the Algebra tab. Then you can choose  a point on the curve.

##### Half-Line

After choosing two points, this menu allows to create a half-line starting at the first point and passing through the second one.

##### Line with given gradient passing through a Point
Choose a point. Then an entry form opens, that allows to enter a formula for the gradient.
##### Perpendicular Bisector
After choosing a segment or two points, this menu allows to create the perpendicular at the middle of this segment.
##### Angle Bisector
Choose three points (side, vertex, side) defining the angle.
##### Locus of a point
Select the point with the mouse and then a free point or a parameter (cursor) on which the point is depending. See onlinehelp or onlinehelp.
##### Regression Line
Draw a rectangle with the mouse enclosing the points to which a line has to be adjusted. See onlinehelp.

#### Curve

This menu allows to import in the Window the graphic representation of a function of Casyopee.

#### Circle

This menu groups the different available manners to create a circle.

##### Circle by Center and Radius by two Points

After choosing three points, this menu allows to create a circle whose the center is the first chosen point ans the radius is the distance between the second and the last chosen point.

##### Circle by Center and passing through a Point

After choosing two points, this menu allows to create a circle whose the center is the first chosen point and the radius is the first and the second chosen point.

##### Circle par Center and algebraic Radius

Choose a point. Then an entry form opens, that allows to enter a formula for the radius.

#### Area

##### Polygon
Successively select at least three points which will be the vertices of the polygon. Then, click the first point again in order to close the polygon.
##### Between curve and line (or between curve and curve).
Allows creating a shaded area between a curve and a line (or between two curves). Select successively the two objects and two points delimiting a vertical  strip between these objects.
##### Angle
Click on three points to create an angle between these points. The second point selected is the vertex of the angle.

#### Transformations

The following buttons create transformations that can be activated through an Image by Affine Transformation button.

Reflection against a point. Choose the center point of the reflection.
Reflection against a line. Choose the line that will be the axis of the reflexion.
Translation. Choose tow points defining a vectore for the translation
Homothetie. Choose a point. Then an entry form opens, that allows to enter a formula for the ratio.
Rotation. Choose a point. Then an entry form opens, that allows to enter a formula for the angle.

Similarity. An entry form opens, that allows to enter a complex definition of the similarity.

General Affine transformations. An entry form opens, that allows to enter a matricial definition of the transformation.

### Create Calculation

This menu entry switches to the Geometrical Calculations Tab and opens the entry form.

### Regression

For a regression other than linear, when a curve is plotted, Casyopee offers to create a geometrical calculation "sum of squared deviations," from a series of points to this curve (the differences is calculated "vertically"). Click thepoints in succession and then click the curve to complete. See onlinehelp.

## Other buttons

### Deplace

Move
After activating this button, you can move any selected free point by dragging them with the mouse.

Move around Point
Select the center point of the rotation first. Then, you may rotate any selected free point around this point by dragging them with the mouse.

### Change Drawing

You may drag and drop the drawing to change the visible area.
Click on any place in the drawing to zoom in. Note: The position of your click determines the center of zoom.

.   Click on any place in the drawing to zoom out. Note: The position of your click determines the center of zoom.

### Image by Affine Transformation

Opens a menu where you can choose a transformation already created. After that, choose the object to apply the transformation. When creating the transformed object, associated points (for instrance extremities of a segment) are also created.