# Split/Merge

These Edit menu commands allow you to alter the relationships of existing objects by splitting points from their parents, by merging points either with other points or onto paths, and by merging pictures or text to points. These commands allow you to fix construction mistakes, to make significant changes in a sketch without starting over, to explore constructions, and to modify geometric and mathematical investigations in flexible and powerful ways.

 Split a Point from Its Parents

You can split a midpoint, point on a path, point of intersection, or plotted point from its parents. Depending on the relationships, the command changes. (For instance, it might Split Midpoint from Segment, Split Intersection from Path Objects, or Split Plotted Point from Coordinate System.)

To split a transformed image point from its pre-image point, you must hold the Shift key while choosing the command.

If the selected point is a point on a path, it’s removed from its path. If the selected point is an intersection point, it’s split from the intersecting objects. If the selected point is a plotted point, it's split from the coordinate system. In each of these cases, it becomes an independent point and can be dragged anywhere.

Split Point from Circle

Split Intersection from Path Objects

 Split a Point from Its Definition

You can split a transformed image point from its definition. Hold the Shift key to enable this command.

The point is split from its pre-image point, and becomes an independent point that can be dragged anywhere. In the first illustration below, the point on the right is a reflected image. In the second illustration, it has been split from its definition as a reflected image, and can be dragged freely.

Split Point from Definition

 Split a Point Apart

You can split an independent point with more than one child into multiple points, one for each child. For example, if you have a point that is the center of a circle and is also the endpoint of two segments, you can split it so that the circle center and segment endpoints are now three separate, unrelated points. Select the point you wish to split and choose Edit | Split Point. The point splits into two or more separate points a small distance from each other.

To split a point apart, you must select an independent point with two or more children.

Split Point

In this example, the center point has three children: the circle and each of the two segments. The Split Point command results in three points: one is the center of the circle and the other two are the endpoints of the segments.

If you want to split the circle center from the two segments while leaving the segments with a common endpoint, first split the point apart and then merge the two segment endpoints.

 Merge Two Points

You can combine two separate points into a single point. Select an independent point and the point to which you want to merge it. One of the points must be independent so that it’s free to merge with the other point. The other point doesn’t have to be independent, but it must not depend on the first.

If the second point could depend on the first, after merging, it would be defined in terms of itself!

Merge Points

Merging two points is a handy way to fix any mistakes you make while using drawing tools.

 Merge a Point to a Path

You can merge a point to a path (straight object, circle, arc, interior, point locus, or function plot) using the Merge command. Select an independent point and a path that doesn’t depend on that point. The point must be independent, and the path must not depend on the point. In this way, for example, you can merge an endpoint of a segment to another segment. After it’s merged, the point is attached to the segment and can move along the segment but cannot leave it (unless you later split it from that segment).

Merge Point to Segment

 Merge Text to a Point

You can merge a text object — a caption, measurement, calculation or function — to a point. To enable this command, hold the Shift key while choosing the Merge command.

1.Select one text object and one point.

2.While holding down the Shift key, choose Edit | Merge Text to Point.

A merged copy of your selected text appears, centered on the point you selected. As you move the point (by dragging it, animating it, or dragging or animating its parents), the merged text moves with it; and as you drag the merged text, the point moves with it. (You may want to hide the point and/or the original measurement to make your sketch more attractive.)

Merge Text to Point

A caption merged to a point can be used to provide a richer description of the point (or the object on which the point is constructed) than can be entered in a label, because you can use the style buttons and Symbolic Notation tools from the Text Palette. A measurement merged to a point can provide a useful visualization of measured properties. For instance, you can merge the measure of an angle to that angle’s vertex or the length of a segment to a (hidden) point on that segment. Note that the copy of your original text merged to the point is not the measurement itself, however. It’s only a display copy of your original measurement. If you want to use the original measurement elsewhere in your sketch (in a calculation, for instance), you should not hide it after merging its text to a point.

Because the merged text is a copy of the original text object, there’s no need to split the text from the point. Instead, make sure that both the original text object and the point are visible, and then delete the merged text object.

 Merge a Picture to a Point

You can merge a picture to a point. Select both the picture and the point, and choose Edit | Merge Picture to Point.

Merge Picture to Point

You can also attach a picture to two or three points, but not by using the Merge command. Instead, select the picture and choose Then select the points and choose

 Split a Picture from One, Two or Three Points

You can split a picture from a point. Select a picture attached to one point and choose Edit | Split Picture from Point.

The picture is separated from the point and no longer moves with it.

You can split a picture from two or three points. Select a picture attached to two or three points, hold the Shift key, and choose Edit | Split Picture from Points.

The picture is separated from the points and no longer moves or changes shape with them.

Split Picture from Point(s)

You can attach a picture to two or three points, but not by using the Merge command. Instead, select the picture and choose Then select the points and choose