Transformation and Symmetry

What is Transformation?

Transformation is defined as the movement of objects in a coordinate plane. A basic transformation is known as the movement of shape in such a way which does not change the size or shape. Transformation is of two categories: –

1. Rigid Transformation

In this transformation, the shape and size of the image will not change.

2. Non-Rigid Transformation

In this transformation, the shape of the image remains shape, but the size of the image gets change.

However, with the rigid and non-rigid transformation, there are more four types of transformation as Rotation, Translation, Dilation, and Reflection.

1. Rotation

It is a process in which an object is rotated without changing the shape and size of an object. In the image below, one can see the Rotation of an object in 90⁰. There different rules of rotations such as

• For 90⁰, the rule states that (x,y) = (-y,x)
• For 180⁰, the rule states that (x,y) = (-x,-y)
• For 270⁰, the rule states that (x,y) = (y,-x)

2. Translation

It is a process in which an object is moving in the space without any change in its shape, size, and orientation. In the image, one can see that the object is moved from its actual position to a new position with affecting the shape, size, and orientation of the object.

3. Reflection

Reflection is a process of flipping an object in line without changing the shape and size of the object. In the image below, one can see the preimage and the image which is formed after reflection.

4. Dilation

Dilation is the process of expanding an image without changing its size, shape, and orientation. In the image below, one can see the dilated triangle.

What is Symmetry?

Symmetry is defined is that when one shape becomesthe same when it is moved in some direction, flipped or rotated. The two imagesare said to be in symmetry if both the objects are having the same shape and size with an object having a different orientation from the first object. Symmetry is also referring to the mirror or reflective symmetry. For example: –In the image, one can see that a Hexagon is divided into two halves and “m” is the line of symmetry. In the image, if left half is reflected across line “m” then the result will be right half. Now, we can say that hexagon is symmetrical about line “m”. In a geometric figure, there can be more than one line of symmetry, or there is no line of symmetry.

Quiz

1. In Transformation a turn is also known as ______________?
2. Reflection
3. Translation
4. Rotation
5. None of these

Answer: -Rotation, is the correct answer.

2. Reflection, Dilation, Translation and Rotations are the part of ____________?
3. Transformation
4. Geometry
5. Measurement
6. All of these

Answer: – Transformation, is the correct answer because these are the types of transformation.

3. Determine the type of transformation from the figure below:

1. Reflection across Y-axis
2. Reflection across X-axis
3. Translation across X-axis
4. Translation across Y-axis

Answer: – Reflection across X-axis, is the correct answer. As in the figure, one can see that the object is flipped across X-axis.

4. Determine the type of transformation from the figure below:
5. Reflection
6. Translation
7. Rotation
8. Dilation

Answer: -Translation, is the correct answer. In the figure above translation of image is occurred 5 units left and 1 unit up because the object shape, size and orientation have not to change with a change of its position so it’s mean is translated.

5. Identify the rule for rotation of 90⁰ is (x, y) =
6. (-y, x)
7. (-x, y)
8. (x, -y)
9. (y, -x)

Answer: – (y, -x), is the correct answer in order to rotate an object in 90⁰.

6. Identify the rule for reflection over y-axis is (x,y) =
7. (-y, x)
8. (y, x)
9. (-y, x)
10. (-x, y)

Answer: -(-x, y), is the correct answer. In order to reflect image in y-axis one has to use rule (x,y) = (-x,y).

7. What is rule for rotation of object in 270⁰ is _______?
8. (x,y) = (-y, x)
9. (x,y) = (y, x)
10. (x, y) = (y, -x)
11. (x, y) = (x, -y)

Answer: – (x,y) = (-y,x) , is the correct answer.

8. The point of Rotation is known as _____________?
9. The point which movesa little bit
10. The point which does not have any origin
11. The point which always on the origin
12. The point which does not move

Answer: -The point which does not move, is the correct answer because it is the centre of the graph on which object rotates.

9. Identify which of the transformation means “to flip”?
10. Dilation
11. Translation
12. Rotation
13. Reflection

Answer: -Reflection, is the correct answer. Reflection is the transformation in which the object is flip across the line without any change of its shape and size.

10. Determine the triangle which has no lines of symmetry?
11. Isosceles Triangle
12. Equilateral Triangle
13. Scalene Triangle
14. None of These

Answer: -Scalene Triangle, is the correct answer as a scalene triangle has only rotational symmetry of order 1 and it does not have equal sides and angles.

11. Determine which figure has two lines of symmetry?

Answer: – option (d) is the correct answer.