Geometric transformations involve taking a preimage and transforming it in some way to produce an image. Transformation can also be defined as the enlargement or reduction of an image without affecting its shape such that the images are similar. The two different types of transformations are rigid transformation, non-rigid transformation. We are giving the important properties of size transformation for the sake of 9th-grade students.
Properties of size Transformation
- The different size transformation properties are listed here:
- The shape of the image after transformation is the same as the original image.
- If the scale factor of the transformation is k, then each side of the image is multiplied by k to get the corresponding measure.
- If k < 1, then the image is reduced from the object and the transformation is said to be a reduction.
- If k = 1, the image is similar to the object and the transformation is said to be an identity transformation.
- If k > 1, the image is enlarged from the object, and the transformation is enlarged.
- If each side of the image is k times the corresponding side of the object, then the area of the image is k² times the area of the object.
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What is Transformation?
Transformation means taking a preimage and transforming it in some way to produce an image. The two different categories of transformations are rigid transformation, non-rigid transformation. There are four types of transformations are rotation, translation, dilation and reflection.
Enlargement transformation means enlarging the object so that the image and object are similar to each other. In the same way, reduction transformation means reducing the size of an object such that the image and object are similar.
The scale factor is a measure that describes how much the shape has been enlarged. For example, a scale factor means that the side lengths of the new shape are twice the side lengths of the original. The scale factor in reduction transformation is the reduction factor.
Problems on Transformation Properties
Problem 1:
A triangle ABC has been transformed into triangle XYZ and their side lengths, AB = 5 m, XY = 10 m, then find the scale factor.
Solution:
Given that,
Triangle ABS has been transformed into triangle XYZ
AB = 5 m, XY = 10 m
Scale factor k = \(\frac { AB }{ XY } \) = \(\frac { BC }{ YZ } \) = \(\frac { CA }{ ZX } \)
k = \(\frac { 5 }{ 10 } \)
k = 1/2
So, the triangle ABC is reduced into triangle XYZ.
Problem 2:
A rectangle PQRS has been transformed into rectangle ABCD and their areas are 150 sq m, 250 sq m respectively. Find the scale factor and determine the transformation is either reduction or enlargement.
Solution:
Given that,
A rectangle PQRS has been transformed into a rectangle ABCD
Area of PQRS = 150 sq cm
Area of ABCD = 250 sq cm
Scale factor k² = \(\frac { Area of rectangle ABCD }{ Area of rectangle ABCD } \)
= \(\frac { 250 }{ 150 } \)
= \(\frac { 5 }{ 3 } \)
k = 1.29
So, the transformation is enlargement.
Problem 3:
A triangle ABC has transformed into triangle DEF and the side lengths of AB = 120 cm, the scale factor is 1. Find side length of DE.
Solution:
Given that,
A triangle ABC is transformed into triangle DEF
AB = 120 cm, the scale factor is 1
Scale factor k = \(\frac { DE }{ AB } \) = \(\frac { EF }{ BC } \) = \(\frac { FD }{ CA } \)
1 = \(\frac { DE }{ 120 } \)
DE = 120
The tranformation is identity and DE = 120 cm.
Frequently Asked Question’s on Properties of size Transformation
1. What is the size transformation?
A transformation changes the shape, size or position of a figure and creates a new figure. A geometry transformation can be rigid or non-rigid.
2. What are the properties of a dilation?
- Each angle of the figure is the same.
- Parallel and perpendicular lines in the figure remain the same as the parallel and perpendicular lines of the dilated figure.
- The midpoints of the figure remain the same as the midpoint of the dilated shape.
- The image remains the same.
3. Which transformation changes the size of an object?
Scaling is a linear transformation that usually makes an object smaller or bigger while maintaining its original shape.
4. What are the 4 types of transformation?
The four main types of transformations are rotation, dilation, translation, and reflection.