centric circles. Reflectionis similar to what we called a “flip” in elementary school
mathematics—like the flip side of an object. One easy way to see this is by noting
one’s reflection in a mirror—the “figure” is on one side of a line and the mirror image
on the other. Reflection twice about two parallel lines is synonymous with translation;
reflection twice about two intersecting lines is called rotation.
Another type of transformation is rotation. This is simple to understand: in ele-
mentary school mathematics it is sometimes called a “turn” or “spin.” In this case,
one point on a plane remains unchanged while keeping all the distances between the
other points the same. Finally, a translation(or glide transformation) is similar to
what is called a “slide” in elementary school mathematics. All the points in the plane
move in the same direction and the same distance; or, the figure slides in a single
direction. Translation is also considered to be reflection twice across two parallel lines.ANALYTIC GEOMETRY
What is analytic geometry?
Analytic geometry is actually another name for coordinate (or Cartesian) geometry, a
way to geometrically represent ordered pairs of numbers (or coordinates). The objects
are described as n-tuples of points, in which n2 in a plane and n3 in a space (or
two and three dimensions) in some coordinate system. Overall, analytic geometry
allows mathematicians to determine the position, configurations, and separations of
objects using algebraic representation and manipulation of equations.What is a graph?
The term graph has several different meanings in mathematics. It can mean the inter-
pretations of numbers, including bar graphs, pie charts, and line graphs. For example,
a pie chart (graph) is often used to represent percents, such as a breakdown of where a
taxpayer’s money is spent in the various government agencies for a certain year.
In analytic geometry, a graph is simply a way of plotting—thus, visually repre-
senting—points, lines, curves, and solids in order to understand and interpret certain
geometric figures and to solve equations. For example, solving an equation with one
to two variables (usually written as xand y,or two dimensions) results in a curve on a
graph (note: a line is considered a curve in geometry). Equations that contain three
variables (usually as x, y,and z,or three dimensions) result in a surface.What is a coordinate system?
A coordinate system is one that uses coordinates—a number or numbers that identify
192 a point on a number line, plane, or in space. These points are most often seen on a