**Introduction to Solve Triangle Transformation:**

A triangle transformation is a change of location of an object on a plane. Generally triangle transformations is a function that is mapping to a set x into another set y or mapping itself, triangle transformation can be classified into two types. They are rigid and non- rigid transformations. there are four main types of triangle transformations are,

- Translation
- Rotation
- Reflection
- Dilation

these four methods are mainly used for solving the triangle transformation .

The mainly basic triangle transformation is the translations. The proper definition of a translation is every point of the pre-image is moved the equal distance in the same direction to form the image.

In solve translation figure, the triangle translated 4 units to the right and 2 units up. Translation can be done in any one direction or two directions. Example for solve translation is

**
T (x, y) = (x + 4, y + 2)**

The distance between the center and any point of the object is same. Around the center point can rotate the objects by an angle. It can be done with the counterclockwise.

In solve rotation picture is a triangle rotated about the center of rotation which is the origin. When the triangle is rotated 90° form a right angle at the origin, the same when rotated 180° these lines forming the same degree of angle at the origin, same happens when rotated 270° . When the triangle is rotated 360° it returns to the original position.

The reflection is a flip of an aim over a line.

The two very common reflections is given by

- Horizontal reflection
- Vertical reflection

In solve reflection picture is a right triangle reflected across the ' y ' axis which is the line of reflection. The pre-image is ΔABC and the image is ΔA'B'C'.

Dilation is used to change the image size. The scale factor is used to measure the image is smaller or greater. **ΔA'B'C'** is the image of **ΔABC** dilated
about **O** with a scale factor 2**.**

**OA' = 2 OA OB' = 2 OB OC' = 2 OC**

Example for solve dilations is **D _{k} ( x , y ) = ( kx , ky ).**