TRANSFORMATIONS
USING MATRICES
In this section, we will learn how we can do transformations using matrices.
Transformations - Definition
A very simple definition for transformations is, whenever a figure is moved from one location to another location, a transformation occurs.
If a figure is moved from one location another location, we say, it is transformation. Our next question is, how can we do the transformation using matrices?. To know that, we have to be knowing the different types of transformations.
Now, let us come to know the different types of transformations.
Different Types of Transformations Using Matrices
There are four main types in transformations using matrices. They are
What is "Image" and "Pre-image"?
When a transformation occurs, the original figure is known as the pre-image and the new figure is known as the image.
It has been clearly shown in the below picture.
Rigid Transformation or Isometry
A transformation where the pre-image and image are congruent is called a rigid transformation or an isometry.
It has been clearly shown in the below picture.
When a figure is moved from one location to another location, we say that it is a transformation.
In this point, always students have a question.
That is, if a figure is moved from one location to another location, we say, "it is transformation". How can this transformation made using matrices ?
More clearly, on what grounds is the transformation made ?
Is there any pre-decided rule to make transformation?
Yes, there is a pre-decided rule to make each and every transformation.
The rule we apply to make transformation is depending upon the kind of transformation we make.
We have already seen that there are four main type of transformations. They are reflection, rotation, translation and dilation.
For example, if we are going to make transformation using reflection, there is a pre-decided rule for that. According to the rule, we have to make transformation.
The rule we apply to make transformation using reflection and the rule we apply to make transformation using rotation.
So, for each type of transformation, we may have to apply different rule.
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WORD PROBLEMS
Word problems on simple equations
Word problems on linear equations
Word problems on quadratic equations
Area and perimeter word problems
Word problems on direct variation and inverse variation
Word problems on comparing rates
Converting customary units word problems
Converting metric units word problems
Word problems on simple interest
Word problems on compound interest
Word problems on types of angles
Complementary and supplementary angles word problems
Trigonometry word problems
Markup and markdown word problems
Word problems on mixed fractrions
One step equation word problems
Linear inequalities word problems
Ratio and proportion word problems
Word problems on sets and venn diagrams
Pythagorean theorem word problems
Percent of a number word problems
Word problems on constant speed
Word problems on average speed
Word problems on sum of the angles of a triangle is 180 degree
OTHER TOPICS
Time, speed and distance shortcuts
Ratio and proportion shortcuts
Domain and range of rational functions
Domain and range of rational functions with holes
Graphing rational functions with holes
Converting repeating decimals in to fractions
Decimal representation of rational numbers
Finding square root using long division
L.C.M method to solve time and work problems
Translating the word problems in to algebraic expressions
Remainder when 2 power 256 is divided by 17
Remainder when 17 power 23 is divided by 16
Sum of all three digit numbers divisible by 6
Sum of all three digit numbers divisible by 7
Sum of all three digit numbers divisible by 8
Sum of all three digit numbers formed using 1, 3, 4
Sum of all three four digit numbers formed with non zero digits
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