Sunday, April 22, 2012

The Elegant Locus

 Aim: The Elegant Locus


Definition: The locus is the set of all points that satisfy a given condition.


- A locus is a general graph of given equation.


- The locus of points equidistant from a single point is set of point, equidistant from the point, in every direction.


- The locus of points equidistant from a single point is a set of points, equidistant from the point, in every direction.

- The Locus of points equidistant from two points is perpendicular bisector of the line segment connecting the two points.

- The locus of points equidistant from a line are two lines, on opposite sides, equidistant and parallel to that line.

- The locus of points equidistant from two parallel lines is another line, half way between both lines, and parallel to each of them.

-The locus of points equidistant from two intersecting lines are two additional lines that bisect the angles fromed by the original lines.

Try now: From Regentsprep.org






The locus of points equidistant from two intersecting lines is ...
Choose:
one circle two parallel lines
two circles a pair of angle bisectors

Sunday, April 15, 2012

Aim: How do we identify solids ?

Aim: How do we identify solids ?

    Solid Geometry: Solid geometry is the geometry of 3-dimensional space.
Properties:
  • Volume
  • Surface Area
Two Main types of solid:
  1. Polyhedra
  2. Non-Polyhedra
Polyhedra: Flat Surface
  • Prism                       
  • Pyramids
  • Platonic solids
Non-Polyhedra: If any surface is not flat
  • Sphere
  • Torus
  • Cylinder
  • Cone
Prisms: Has the same cross section all along its length
Cross sections: The shape you get when you cut straight down
Surface Area: The area of the bases + the Lateral Area ( area of the side)