How To Construct a Segment of Fixed Length

How To . . . Construct a Segment of Fixed Length

Occasionally you may wish to create a segment of fixed length—for instance, a segment that is exactly 1.5 cm in length. While you could create a segment with the Segment tool, measure its length, and drag one endpoint until its length was 1.5 cm, this segment would not be constructed to be fixed at 1.5 cm long. That is, dragging an endpoint again would change it from its current length to some other length.

To fix a segment’s length in Sketchpad, you need to construct the segment in such a way that dragging cannot change its length. For an arbitrary length, the easiest way to do this is with the Transform menu.

1. Create a point A in your sketch.

2. Select point A and choose Translate from the Transform menu. In the dialog box, enter the fixed length as the distance by which you wish to translate point A.

3. Click on Translate.

Sketchpad constructs a new point A' as the translated image of A by the distance that you entered (1.5 cm). Now use the Segment tool to construct the segment between A and A'. No matter how you drag either endpoint, the segment’s length will remain 1.5 cm because it has been constructed to always have that length.

Note that these steps give you a fixed length and a fixed orientation. If you want a segment of fixed length whose orientation you can change, construct a circle with radius AA'. Then draw a second radius from A to any point B on the circle. Segment AB can now be dragged to any orientation while always having a fixed length, because all radii of the circle have the same length and the circle is constructed to always have a radius of fixed length AA'.