subject: Triangle Transformations [print this page] Transformations is a change of position of an object on a plane. Generally there are four types of transformations are occur in the triangle
Translation
Rotation
Reflection
Glide reflection
After the completion of this transformation the shape of the object still has the same size, angles, and line lengths. Suppose if any shape can become another using those transformation, then the two shapes are called Congruent.
Isometric Transformations :
Based on the isometric it can be classified into three types, they area
Isometric Transformation
Direct Isometric Transformation
Opposite Isometric Transformation
Isometric Transformation:
A transformation is an isometric transformation if it preserves its distance. An isometric transformation can be either direct isometric transformation or opposite isometric transformation.
Direct Isometric Transformation
An isometric transformation is direct if it preserves distance and orientation (direction).
Opposite Isometric Transformation:
An isometric transformation is opposite if it preserves but fails to preserve orientation.
Triangle Transformations:
It means we can move the object from one plane to another plane only the object will be move it differs from rotation and reflection generally every translation has a direction and distance.
Transformations, as the name suggests, change things - usually, as far as you're concerned, triangles on a graph.
The 4 main transformations (and the ones you need to know about) are Reflection, Rotation, Enlargement and Translation.
Despite its name, this doesn't require a great deal of thought! You simply have a line of reflection and move every point on the shape the same distance away on the other side of the line.
If you're doing a reflection on a graph the mirror line may be given as an equation or it might just be the x-axis or the y-axis.
If the mirror line equation is x =..... then it is a vertical line through that number on the x-axis.
If the mirror line equation is y =..... then it is a horizontal line through that number on the y-axis.
y = x is the diagonal line going through (0, 0), (1. 1), (2, 2), etc.
y = -x is the diagonal line going through (0, 0), (1, -1), (2, -2), etc.
Important: Don't try to reflect whole shapes all at once. Reflect each corner on the shape then draw the reflection by joining the points you've reflected.
Example:
Translation of triangle ABC
In the above figure the triangle ABC has been moved from position I to position II
As triangle ABC.we can see that A has moved 3 units along and 4 units up in order to coincide with A
Rotation:
Rotation of the object means it will be turn it around; basically every rotation has the center and the angle of rotation ,in the rotation there is no change in shape ,size but there is change in the position .
Consider the object as it moves the rotation of angle 90degree
Reflection:
To reflect an object means to produce the mirror image.
Every reflection has a mirror line. A reflection of the object R is shown in figure
Glide reflection:
A glide reflection it always combines a reflection with a translation along the direction of the mirror line
It is the only transformation it contains more than one step.
