MENZAHIRKAN PELAJAR BERTARAF DUNIA
A set is a collection of objects, things or symbols which are clearly defined.
The individual objects in a set are called the members or elements of the set.
A set must be properly defined so that we can find out whether an object is a member of the set.
There are two ways of doing this.
1. Listing the elements
The set can be defined by listing all its elements, separated by commas and enclosed within braces.
Example:
B = {2, 4, 6, 8, 10}
X = {a, b, c, d, e}
However, in some instances, it is impossible to list all the elements of a set. In such cases, we define the set by method 2.
2. Describing the elements
The set can be defined, where possible, by describing the elements.
Example:
C = {x : x is an integer, x > – 3 }
This is read as: “C is the set of elements x such that x is an integer greater than –3.”
D= {x: x is a river in a river}
We should describe a certain property which all the elements x, in a set, have in common so that we can know whether a particular thing belongs to the set.
We relate a member and a set using the symbol ∈. If an object x is an element of set A, we write x ∈ A. If an object z is not an element of set A, we write z ∉ A.
∈ denotes “is an element of’ or “is a member of” or “belongs to”
∉ denotes “is not an element of” or “is not a member of” or “does not belong to”
Example:
If A = {1, 3, 5} then 1 ∈ A and 2 ∉ A
Translations - Each Point is Moved the Same Way
The most basic transformation is the translation. The formal definition of a translation is "every point of the pre-image is moved the same distance in the same direction to form the image." Take a look at the picture below for some clarification.
Each translation follows a rule. In this case, the rule is "5 to the right and 3 up." You can also translate a pre-image to the left, down, or any combination of two of the four directions.
More advanced transformation geometry is done on the coordinate plane. The transformation for this example would be T(x, y) = (x+5, y+3).
Reflections - Like Looking in a Mirror
A reflection is a "flip" of an object over a line. Let's look at two very common reflections: a horizontal reflection and a vertical reflection.
Notice the colored vertices for each of the triangles. The line of reflection is equidistant from both red points, blue points, and green points. In other words, the line of reflection is directly in the middle of both points.
Examples of transformation geometry in the coordinate plane...
Reflection over x-axis: T(x, y) = (x, -y)
Reflection over y-axis: T(x, y) = (-x, y)
Reflection over line y = x: T(x, y) = (y, x)
A rotation is a transformation that is performed by "spinning" the object around a fixed point known as the center of rotation. You can rotate your object at any degree measure, but 90° and 180° are two of the most common. Also, rotations are done counterclockwise!
The figure shown at the right is a rotation of 90° rotated around the center of rotation. Notice that all of the colored lines are the same distance from the center or rotation than than are from the point. Also all the colored lines form 90° angles. That's what makes the rotation a rotation of 90°.
More transformation geometry in the coordinate plane...
Rotation 180° around the origin: T(x, y) = (-x, -y)
