All questions of Transformations and Symmetry for Grade 9 Exam

Only 2 lines of symmetry can be drawn in a rectangle. one is vertical and another is horizontal. carners lines are incorrect.

Because square has 4 lines . If we draw symmetry in the centre of square the lines are also four 2 right side and 2 left side

No , answer none of this

Correct answer is option 'a' as H is horizontally and vertically symmetrical if we draw a line between H vertically and horizontally across it.

An object is formed by reflecting the object in a mirror. It is a reversed and flipped version of the original object. The mirror image appears to be behind the mirror and is identical in shape and size to the original object, but with the left and right sides switched.

There is only one line of symmetry in an isosceles triangle as only two sides of a triangle are equal in length. Thus, the correct answer is choice (b).

The answer is B.

Regular hexagon means the all sides of hexagon are equal.

Understanding Symmetries
When analyzing quadrilaterals, it's essential to understand what line and rotational symmetries are:
- Line Symmetry: A shape has line symmetry if it can be divided into two identical halves by a straight line.
- Rotational Symmetry: A shape has rotational symmetry if it can be rotated around a central point and still look the same at certain angles.
Symmetries of Given Quadrilaterals
Let's examine each option based on these definitions:
- A Triangle:
- A triangle can have line symmetry (like an equilateral triangle) but generally has rotational symmetry of order 1 (it only looks the same when rotated 0 degrees).
- A Square:
- A square has 4 lines of symmetry (through the midpoints and corners) and a rotational symmetry of order 4 (it looks the same at 90°, 180°, 270°, and 360°). This is the only quadrilateral in this list with both line and rotational symmetries of order more than 3.
- A Kite:
- A kite has 1 line of symmetry but only has rotational symmetry of order 1 (it does not look the same when rotated).
- A Rectangle:
- A rectangle has 2 lines of symmetry (through the midpoints) and a rotational symmetry of order 2 (it looks the same at 180° but not at smaller angles).
Conclusion
The only quadrilateral from your list that possesses both line and rotational symmetries of order more than 3 is the square. Thus, the correct answer is option B (the square).

C

Explanation:
A horizontal line of symmetry means that a figure can be divided into two equal halves by a line that is parallel to the ground. Let's analyze each alphabet one by one to determine if it has a horizontal line of symmetry:

a) C:
The alphabet "C" has a curved shape, but it does not have a horizontal line of symmetry. If we try to draw a horizontal line through the middle of the "C", the two halves will not be equal.

b) K:
The alphabet "K" consists of two diagonal lines joined at a vertical line. It does not have a horizontal line of symmetry because a horizontal line cannot divide it into two equal halves.

c) D:
The alphabet "D" has a rounded shape with a straight vertical line. It does have a horizontal line of symmetry. If we draw a horizontal line through the middle of the "D", the two halves will be equal.

d) All the above:
Since both "C" and "K" do not have a horizontal line of symmetry, the correct answer is option 'D', which states that all the above alphabets do not have a horizontal line of symmetry.

In conclusion, only the alphabet "D" has a horizontal line of symmetry.

The angle of rotation of a shape refers to the degree by which the shape needs to be rotated to coincide with its original position. In this case, a square has a rotational symmetry of order 4, which means it can be rotated by a certain angle multiple times to align with itself.

To determine the angle of rotation, we need to consider the number of times the square can be rotated to achieve symmetry. Since the rotational symmetry of order 4 means the square can be rotated four times to match its original position, we can calculate the angle of rotation by dividing a full circle (360 degrees) by the number of rotations.

Let's break down the steps to find the angle of rotation:

Step 1: Determine the number of rotations for symmetry
In this case, the square has a rotational symmetry of order 4, which means it can be rotated four times to align with itself.

Step 2: Calculate the angle of rotation
To find the angle of rotation, we divide a full circle (360 degrees) by the number of rotations.
360 degrees ÷ 4 rotations = 90 degrees

Therefore, the angle of rotation for the square with rotational symmetry of order 4 is 90 degrees.

Option B, which states that the angle of rotation is 90 degrees, is the correct answer.

Line of Symmetry in Alphabets

Symmetry in Alphabets:
Symmetry is a key concept in mathematics and can be observed in various shapes and figures, including alphabets. A line of symmetry divides a shape into two identical halves, mirroring each other.

Alphabets with Symmetry:
- Alphabets like A and O have a line of symmetry. When folded along the line of symmetry, both halves match perfectly.

Alphabets without Symmetry:
- The alphabet P does not have a line of symmetry. If you try to fold the alphabet P along any axis, the two halves will not match perfectly.

Explanation:
When we look at the alphabet P, we can see that it has a curved shape with a vertical line on one side. This vertical line acts as a distinguishing feature that prevents the alphabet P from having a line of symmetry. No matter how we try to fold the alphabet P, the two halves will not coincide perfectly.

Conclusion:
In summary, out of the alphabets mentioned (A, B, P, O), the alphabet P is the one that does not have a line of symmetry. This lack of symmetry is due to the specific shape and design of the alphabet P, making it distinct from the other alphabets mentioned.

Understanding Reflectional Symmetry
Reflectional symmetry, also known as mirror symmetry, occurs when one half of an object is a mirror image of the other half. In the case of the letter 'E', we can analyze its symmetry by considering how it would appear if reflected in a mirror.
Vertical vs. Horizontal Reflection
- Vertical Mirror: If we place a vertical mirror on the left or right side of the letter 'E', the two halves created by the mirror will look identical. The vertical line divides 'E' into two symmetrical parts, with the top, middle, and bottom lines remaining parallel and in the same arrangement.
- Horizontal Mirror: If we attempt to reflect 'E' using a horizontal mirror (above or below), the top and bottom sections do not align. The top arm of 'E' would appear at the bottom in the reflection and vice versa, which breaks symmetry.
Conclusion
Thus, the letter 'E' only exhibits reflectional symmetry when using a vertical mirror. The correct answer to the question is option 'B', as the shape of 'E' maintains its structure and symmetry only when reflected vertically. This understanding illustrates the importance of reflectional symmetry in recognizing and analyzing shapes in geometry.

A square has 4 lines of symmetry vertically,horizontally,diagonally

The wheel moves in 360 turn so the symmetry is 4

The given figure is a six-pointed star, which has rotational symmetry of order 6. This means the figure looks the same after a rotation of 360°/6 = 60° about its center. Therefore, the order of rotational symmetry is 6.