## High School Geometry with Geometric Algebra

Previous section: Modeling Real Objects and Motions with Vectors.

Next sectionBasic Kinematic Models of Particle Motion.

Nonparametric equation for a line {x} through point a with direction u:    (x a u = 0.

Exercises:

(1)  Sketch the line.

(2)  Derive an equivalent parametric equation for the line with  u2 1.

(3)  Find the directed distance d from the origin 0 to the line and sketch.

(4)  Find the directed distance from an arbitrary point y to the line.

Hints:

(2)  Write  (xa)= α  and solve for  x αa.

(3)  xadu. Sketch the directed areas and solve for d

(

Rigid displacements in a plane: Congruence and measurement

Equations for a rigid displacement of particles in a body or points in a reference frame:

x x′ = Ra                    eiθ          R eiθ

y y′ = Ra

Rigid displacement of an interval:

r = x y    →    r′ = x′ − y′ = R(x y)

or

r′ = Rr = rR

Invariants of rigid displacements:  Euclidean distance:    (x′ − y)2 (− y)2

Previous sectionModeling Real Objects and Motions with Vectors.

Next section: Basic Kinematic Models of Particle Motion.