Move point C and observe what happens.
The green trace generated by point D is a parabola. A parabola is the set of points equidistant from a given point (focus) and from a given point (directrix). In the applet above, point B is the locus and the red line is the directrix.
Use the tangrams below to construct a square. Drag the interior of the polygons to move them and drag the point to rotate.
Move point C about the circle. Observe what happens to point P.
- What can you say about the lengths of segment CD and segment PE?
- What can you say about the distance of E from the origin? What is it equal to?
- What do x and y represent in P(x,y)?
- What do the traces of P represent?
The applet below is a simulation of rolling of two dice. Click the Roll Dice button to roll the dice. Do this 30 times and record the sum. What do you observe?