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## Part 1. Construct the Linkage

Construct the linkage as follows. Once you have a sketch, make this procedure into a script.

2. Use Translation by Fixed Cartesian on the endpoints of one of the segments you just constructed to get U and T.

3. You can now construct P. The only requirement is that P is a specified distance from U. How can you construct it?

4. How do you determine the placement of R and S? Remember that they are both a specified distance from T and a specified distance from P. Construct them.

5. To determine the placement of Q, what do you know about a polygon with four sides of equal length? Mathematically, you could construct Q using either intersections of parallel lines or intersections of circles. However, for technical reasons, intersections of parallel lines works better. Construct Q.

6. After completing your sketch, move P while you trace P and Q to form conjectures as to the shapes their traces lie on.

7. Change the lengths of the three segment and move P while you trace P and Q again. Does your conjecture remain true?

By now you have formulated a conjecture for the shape traced by Q as P moves. The next question is: Why do P and Q behave as they do? In the next section, you will learn about inversion. In part 3, you apply this knowledge to your linkage to understand why P and Q move as they do.

Next: Inversion