You may want to select multiple objects within the TI-Nspire Geometry application for two reasons. First, multiple selected objects can be translated. Second, all selected objects can be deleted by pressing the [DEL] key once.
To move all objects on a screen, move your cursor to open space and press [CTRL][CLICK]. You see the crunched-up paper symbol, indicating that all objects on the screen can be translated using the Touchpad. See the first screen.

Here are two methods that can be used to select multiple objects:
Method 1:
Move to an object and press [CLICK]; it will begin to flash.
Continue moving to additional objects, pressing [CLICK] each time until they begin to flash.
To deselect individual objects from a group, move the cursor to the desired object and press [CLICK]. To deselect all objects, press [ESC].
Method 2:
Press [MENU]→Actions→Select to invoke the Select tool.
Consider a rectangle surrounding the objects that you want to select. Move to one of the vertices of this rectangle and press [ENTER].
Move to the opposite corner of this rectangle and press [ENTER] again to select the group of objects.
Any object that is even partially contained within the rectangle is selected. See the second screen.
After objects have been selected, press the [DEL] key to delete them.
To move selected objects, simply use the Touchpad keys. Alternatively, move the cursor to one of the selected objects, grab the object ([CTRL][CLICK]), and use the Touchpad to move the group. See the third screen.
If you want to delete all objects in an application, press [MENU]→Actions→Delete all. Press [ENTER] at the warning prompt to delete the objects, or press [ESC] if you decide against it.