Math 487 Lab 2: Distance from Lines

Sketchpad Lore: Read this first

Distance from a Point to a Line

  1. Work through Exp 5.2, Investigation 2: Construction – Distance Slider
  2. Continue the same Investigation 2: Construction – Other Measurements

What you should take away from this is a set of answers to these questions:

  1. In a right triangle, why is the right angle the largest angle?

  2. In a right triangle, why is the hypotenuse the longest side?

  3. Why is the shorted distance from a point C to the points on a line AB given by the distance from C to the foot E of the perpendicular from C to line AB?

  4. Explain why the figure with the circle in this investigation illustrates visually the point above. Why does the line AB intersect the circle only at one point E.

Strip

For this part, you should download a Sketchpad file at this link.

Work through the GSP file and compare with Exp 5.3, Investigation 1: Within an Inch of a Line. 

A key point here is that the edge of the trace is the set of points at exactly distance d from the object. so the set of points at exactly distance d from a line consists of a pair of lines parallel to the given line. We call the figure of two lines a STRIP.

  1. Create a tool to construct a strip from its midline and a segment representing distance. This is described n Exp 5.3, Investigation 2: Scripts for Strips in the section Construction – A Strip and its Midline.

Ripples, Strips, and Inscribed Circles

  1. Work through the first 3 pages of Exp 5.3, Investigation 3, Ripples, Strips, and Inscribed Circles.  These investigations are about two intersecting strips.

What you should carry away from this is the ability to answer Q1, Q2, Q3, Q4

  1. Continue with the rest of Exp 5.3, Investigation 3:

Note the answers to Q1, Q2, Q3.  These are the Major Conclusions from the Lab.