MathDB

Given two points

P,Q

of the plane, denote

P+Q

the midpoint of (possibly degenerate) segment

PQ

and

P\cdot Q

the image of

P

in rotation around the origin

Q

under

+90^\circ.

a) Are these operations commutative? b) Given two distinct points

A,B

the equation

Y\cdot X=(A\cdot X)+B

defines a map

X\mapsto Y.

Determine what the mapping is. c) Construct all fixed points of the map from b).

Problem Statement