In the following figure P is the mid-point of BC. [br]Construct the figure and find the locus of P when C moves.

Construct the following figure and find the locus of M, the mid-point of PE, when P moves on the sides of the rectangle ABCD.

Modify the figure in the previous task to the figure below.[br]Observe the locus of M when M is at difference positions on EP.[br]Trace the locus of M when t changes.