## Key Concepts

- How to draw similar triangle
- Dilation
- Draw dilated image
- Identify the dilation undergone for a particular image

### Understanding Dilation

Dilation is a transformation that stretches or shrinks a figure to create a similar figure. It is a similarity transformation.

Center of Dilation: A fixed point with respect to which a figure is enlarged or reduced is the center of dilation.

Scale Factor of Dilation: The scale factor of a dilation is the ratio of a side length of the image to the corresponding side length of the original figure.

If the scale factor is greater than 1 then the dilated image has enlargement and if the scale factor is less than one dilated image had a reduction.

If the scale factor is greater than 1 the dilated image stretches and if the dilated image is less than 1 the dilated images Shrinks.

In the transformation dilation, we get similar images or the images are similar

Coordinate notation of dilation with respect to the origin is (x, y) ® (kx, ky)

### Similar triangle construction

Given a triangle ABC in a coordinate plane. To construct a similar triangle to ABC:

- Draw line segments from the origin passing through the vertices of triangles.
- Mark points D, E, F from A,B,C from distance equal to OA,OB,OC respectively.

- oin the points D, E, F to get similar triangle DEF.

#### Draw a dilation with scale factor 2 for a polygon with vertices *K*(-1, 0), *C*(1, 2), *U*(0, -2)

#### Write the rule of dilation for the following figure

The vertices of the given figure are K(4,0), Z(2,1), M(4,4) and the vertices of the dilated figure are K’(2,0) ,Z’(1,0.5), M’(2,2)

Rule of dilation is (x, y) ® (1 / 2x,1 / 2y)

## Exercise

- Draw a dilation of scale factor 2 with given coordinates
- Find the coordinates of dilated image of the points X(4,4), Y(2,-1), Z(4,-1)with scale factor ¼.
- Write the rule for the dilation from U(-2,-1), K(0,2), F(2,-2) to U’(-3,-1.5), K’(0,3), F’(3,-3)
- Find the scale factor of dilation from figure A to Figure B

- Draw a dilation of polygon with vertices A(-2, 1), B(-4, 1), C(-2, 4) and scale factor k = 2
- If A and B are similar triangles then find the value of m and n

### Concept Map

### What we have learned

**What is transformation?**

- Transformation is a change.

**What is dilation?**

- Dilation is a transformation that stretches or shrinks a figure to create a similar figure. It
- is a similarity transformation.

**What is a scale factor?**

- The scale factor of a dilation is the ratio of a side length of the image to the corresponding side length of the original figure.

**What is the center of dilation?**

- A fixed point with respect to which a figure is enlarged or reduced is the center of dilation.

#### Related topics

#### Composite Figures – Area and Volume

A composite figure is made up of simple geometric shapes. It is a 2-dimensional figure of basic two-dimensional shapes such as squares, triangles, rectangles, circles, etc. There are various shapes whose areas are different from one another. Everything has an area they occupy, from the laptop to your book. To understand the dynamics of composite […]

Read More >>#### Special Right Triangles: Types, Formulas, with Solved Examples.

Learn all about special right triangles- their types, formulas, and examples explained in detail for a better understanding. What are the shortcut ratios for the side lengths of special right triangles 30 60 90 and 45 45 90? How are these ratios related to the Pythagorean theorem? Right Angle Triangles A triangle with a ninety-degree […]

Read More >>#### Ways to Simplify Algebraic Expressions

Simplify algebraic expressions in Mathematics is a collection of various numeric expressions that multiple philosophers and historians have brought down. Talking of algebra, this branch of mathematics deals with the oldest concepts of mathematical sciences, geometry, and number theory. It is one of the earliest branches in the history of mathematics. The study of mathematical […]

Read More >>#### How to Solve Right Triangles?

In this article, we’ll learn about how to Solve Right Triangles. But first, learn about the Triangles. Triangles are made up of three line segments. These three segments meet to form three angles. The lengths of the sides and sizes of the angles are related to one another. If you know the size (length) of […]

Read More >>
Comments: