Google Classroom
GeoGebraGeoGebra Classroom

Khayyam 1

  1. Note the line f passing through points A and B and the line t, a perpendicular to f passing through B.
  2. Draw a point C on the line f, making sure that B is between C and A (so if A is "above" B, your point is "below"  B)
  3. Draw a circle with diameter AC. (Hint: Using the midpoint tool, (the three dots) find the midpoint of AC. -Geogebra will denote the midpoint by D)
  4. Mark the two points where  circle intersects the line t. (A good way to do this is using the intersection tool, next to the point tool). The intersection points are denoted by E and F.
  5. Construct a perpendicular to the line t through E, and a perpendicular to the line t through C.
  6. Find the intersection point of these two lines. (This point is denoted by G)
  7. Now, using the "locus tool" (next to the delete tool) find the locus of points that can be found with this procedure when the point C moves. (After clicking the locus tool, click on the point G, intersection of the two lines, and then the point C)
  8. Repeat the construction of the previous paragraph, on the other side of the line f.
  9. Answer the Slido questions  (and if you have time try to prove why the curve you found is indeed such curve)