Translations

A translation is the movement of an object a certain distance in a certain direction. To define a translation we need to define a vector.  A vector is defined by a magnitude and a direction. A translation based on a vector will move objects in the direction given by the vector over a distance determined by the magnitude of the vector.

Vectors can be defined in three ways: by a pair of points, by a pair of points and an angle, and by two numerical values.

To define a vector by a pair of points, we first select two points and then choose "Vector" under the "Mark" menu. A dialog box will pop up asking us if we are trying to define a vector in rectangular or polar form.  In rectangular form two points uniquely define a vector, so we choose "Rectangular".  Then, we can translate any object by this vector. In the figure below, points 1 and 2 were set as a vector. Then, after selecting the triangle A,B,C the translate button becomes active. When we click on this tool, the original triangle is copied and translated by the vector that we defined. At this point if we changed the vector (1,2) the translated triangle would also change.

translate


To define a polar vector we need a distance and an angle.  To define a distance, again select two points and choose "Vector" under the "Mark" menu. When the vector dialog box pops up this time, select "Polar." Next, we need to define an angle. To do this select three points to define an angle. Then, select "Angle" under the "Mark" menu. We can now translate any object by this polar vector.  In the figure below the triangle A,B,C is being translated a distance given by (D,E) in the direction determined by the lower right angle (F,G,H) (about 90 degrees).  If we now change either the segment (D,E) or the angle, the translated triangle would dynamically change as well.

polar translate
There is one final method to determine a vector. In this method we define the translation in terms of two numerical values - the magnitude and direction (in other words the polar values for a vector).  To do this, select "Translation" from the "Custom" menu. Then, set the magnitude (the distance that the translation will cover) and the direction (the angle (in degrees) that the translation vector makes with the horizontal).  Then, objects such as the triangle above can be translated by this static vector.