Similarity and Transformations

Translation is the movement of function horizontally or vertically.

When a function y=f(x) is translated vertically by b units then translated function is y-b=f(x)

When a function y=f(x) is translated horizontally by a units then translated function is y=f(x-a)

A few examples stating the above were illustrated in detail.

Scaling is multiplying function with some constant.As the function y=f(x) is multiplied by constant c it becomes y=c f(x). Under this heading, a few examples are explained.

Dilation is the similarity transformation in which the figure is enlarged or reduced according to the scale factor without altering the shape and center of image.

In dilation each point move along the straight line which is drawn from the fixed point, center of dilation and the distance point moves depend on the scale factor.

There are two types of Dilations

• Enlargement
• Reduction

The properties of dilations are shown in detail. Also, a few solved examples on Dilations were discussed.

Reflection of any object is the mirror image of that object across the mirror line. Mirror line also called as central line. Every point of the image is at the same distance as object from the mirror line. Reflection has the same size as original image. The types of reflection and a few steps to make the reflected image were also discussed under this heading.

In a translation, a polygon is moved to a new position in such a way that all points on the polygon move the same distance in the same direction, so that the new shape has exactly the same orientation as the original shape. In this heading, we see a few solved examples and also the properties of translated object.

Rotation means the turning of object around the center. Every rotation has a center and angle of rotation. By convention positive rotation go counterclockwise and negative rotation goes clockwise. A few solved examples of Rotation by 180 degree origin as the center and Rotation by 270 degree origin as the center are also shown.

The ratio of the perimeters of similar figure is equal to the ratio of the corresponding sides. The proof of this statement is also explained with examples. A few Solved Problems on Perimeter of similar figure are explained here. The ratio of the areas is equal to the square of the ratio of the corresponding sides. The proof of this statement is also explained with examples.

Two polygons whose corresponding angles are congruent and corresponding sides are in equal proportion are called similar polygon. A few properties of similar polygons are explained with examples.

Triangle which contain right angle is called right triangle and the side opposite to right triangle is called hypotenuse. Rest of the sides is called legs. The Similarity theorems of right triangles are as follows:

Leg Leg theorem

Leg - Acute angle theorem

Hypotenuse - Acute angle theorem

Hypotenuse - Leg theorem

A few examples are shown for the above theorems.

Examples on Similarity and transformations, Understanding Similarity and transformations, Concepts on Similarity and transformations