# Symmetry Questions

We provide symmetry practice exercises, instructions, and a learning material that allows learners to study outside of the classroom. We focus on symmetry skills mastery so, below you will get all questions that are also asking in the competition exam beside that classroom. #### List of symmetry Questions

Question NoQuestionsClass
1The image of the point (1,6,3) in the ( operatorname{line} frac{x}{1}=frac{y-1}{2}=frac{z-2}{3} ) is?
A. (1,0,7)
в. (7,0,1)
c. (2,7,0)
D. (-1,-6,-3)
7
2How many lines of symmetry are there in a triangle which has all the angles equal?
A . 1
B . 2
( c .3 )
D. 4
7
3Find the order of rotational symmetry of rhombus.
A . 4
B. 3
( c cdot 2 )
( D )
7
4Find the number of lines of symmetry in the figure.
( A )
B. 2
( c cdot 3 )
( D )
7
5What is the smallest number of squares
that must be added so that the line PQ
becomes a line of symmetry?
( mathbf{A} cdot mathbf{5} )
B. 3
( c cdot 4 )
( D )
7
6State the number of lines of symmetry for the following figures
(a) An equilateral triangle
(b) Isosceles
triangle (c) Scalene triangle
(d) A square
(e) A rectangle
(f) ( A ) rhombus
(g) A parallelogram
(h) A
(i) A regular hexagon (j) A circle.
7
7Draw, wherever possible, a rough sketch
of:

A triangle with only line symmetry and
no rotational symmetry of order more
than 1

7
8How many lines of symmetry does this star have?
( A cdot 2 )
B. 5
( c cdot 4 )
( D )
7
9Match the following.
Order of rotational
symmetry
( (P) )
(i) 5
( (mathrm{Q}) )
(ii) 2
( (mathbf{R}) )
(iii) 3
( (mathbf{S}) )
(iv) 4
( mathbf{A} cdot(mathrm{P}) rightarrow(mathrm{iv}),(mathrm{Q}) rightarrow(mathrm{i}),(mathrm{R}) rightarrow(mathrm{i}),(mathrm{S}) rightarrow(mathrm{iii}) )
B. ( (P) rightarrow(text { iv) },(Q) rightarrow(text { iii) },(R) rightarrow(text { ii) },(S) rightarrowtext { (i) } )
C. ( (P) rightarrow(text { ii) },(Q) rightarrow(text { iv }),(R) rightarrow(text { iii) },(S) rightarrow(i) )
( mathbf{D} cdot(mathbf{P}) rightarrow(mathbf{i} mathbf{i}),(Q) rightarrow(mathbf{i}),(R) rightarrow(i mathbf{v}),(S) rightarrow(text { iii }) )
7
10List the coordinates of the vertices of
the larger shape
7
11Name a triangle which has exactly one
line of symmetry. Show line of symmetry in figure.
7
12Find the value of the solid obtained by
the complete revolution of the ellipse ( frac{x^{2}}{36}+frac{y^{2}}{25}=1 ) about ( x- ) axis.
7
13Draw a quadrilateral that have four
lines of symmetry.
7
14toppr
( A )
B.
( c )
( D )
7
15Give the order of the rotational
symmetry for each figure:
7
16The no-of order of rotational symmetry
of B, E, D?.
7
17Let ( 0<alpha<frac{pi}{2} ) be a fixed angle. If ( P= )
( (cos theta, sin theta) ) and ( Q=(cos (alpha- )
( boldsymbol{theta}), sin (boldsymbol{alpha}-boldsymbol{theta})) ) then ( boldsymbol{Q} ) is obtained from
( P ) by
A. clockwise rotation around the origin through an angle
B. anticlockwise rotation around the origin through an angle ( alpha )
c. reflection in the line through origin with slope ( tan alpha )
D. reflection in the line through the origin with slope ( tan (alpha / 2) )
7
18The number of line symmetries that the
given figure have- –
( A )
B. 3
( c cdot 2 )
D.
7
19How many lines of symmetry are there in a regular octagon?7
20Rectangle ABCD is the image of
rectangle ABCD after which of the
following rotations?
A ( cdot ) A ( 90^{circ} ) clockwise rotation about the origin
B. A ( 180^{circ} ) rotation about the origin
C. ( A 90^{circ} ) counterclockwise rotation about the origin
D. A ( 90^{circ} ) counterclockwise rotation about the point (1,1)
7
21The number of line symmetries that the given figure have- –
( A cdot 2 )
B. 4
( c .3 )
D.
7
22The order of rotational symmetry of a ceiling fan with 3 blades is
A . 2
B. 3
( c cdot 4 )
( D cdot 6 )
7
23If ( boldsymbol{P}=(8,6) ) and ( mathrm{R} ) is the rotation
through ( 90^{circ} ) about ( 0, ) then ( R_{-90} O(P) ) is
A. (6,-8)
()
в. (-8,-6)
( c cdot(8,6) )
D. (-8,6)
7
24Can you draw a triangle having: no line
of symmetry.
7
25The number of lines of symmetry for a
line segment
A. Is infinite
B. One
c. Two
D. None
7
26begin{tabular}{|c|}
hline \
hline \
hline \
hline \
hline \
hline
end{tabular}
7
27Statement-1:
The point ( A(1,0,7) ) is the mirror image of the point ( B(1,6,3) ) in the line ( frac{x}{1}= ) ( frac{y-1}{2}=frac{z-2}{3} )
Statement-2:
The line: ( frac{x}{1}=frac{y-1}{2}=frac{z-2}{3} ) bisects the
line segment joining ( A(1,0,7) ) and ( B(1,6,3) )
A. Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for statement- -1
B. Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-
c. Statement-1 is true, Statement-2 is false
D. Statement-1 is false, Statement-2 is true
7
28Point ( P(6,6) ) lies on the circle with
center (2,3) and radius 5 coordinate
units. Find the co-ordinates of the
image of point ( mathrm{P} ) after the circle is
rotated ( 90^{circ} ) clockwise ( ( circlearrowright ) ) about its
center.
A ( .(2,3) )
B. (3,2)
( c cdot(5,-1) )
( D cdot(6,0) )
E. (7,3)
7
29n the given figure, which of the
following is a line of symmetry?
A. Line A
B. Line B
c. Line A and B
D. Line
7
30What other name can you give to the
line symmetry of:
an isosceles triangle
7
31What is the order of rotational
symmetry of a regular pentagon?
A . 2
B. 5
c. 10
D. 15
7
32The order of rotational symmetry for the given figure is
A. 3
B. 4
( c cdot 6 )
( D cdot 12 )
7
33What is the order of rotational
symmetry of rectangle?
( A )
B. 2
( c cdot 3 )
( D )
7
34The order of rotational symmetry for the given figure is
( A cdot 4 )
B. 3
( c cdot 2 )
( D )
7
35The lines of symmetry of a ( -ldots—- ) are the lines joining the mid-points of the opposite sides.
A. square
B. triangle
c. rectangle
D. isosceles
7
36What is the smallest number of squares
that must be added so that the line ( A B )
becomes a line of symmetry?
( A )
B. 2
( c .5 )
D.
7
37Find the coordinates of the foot of
perpendicular drawn from the point ( A(-1,8,4) ) to the line joining the points ( B(0,-1,3) ) and ( C(2,-3,-1) . ) Hence,
find the image of the point ( A ) in the line
( boldsymbol{B C} )
7
388 different shapes are given in the
following figure. How many shapes have
0 lines of symmetry?
7
39The image of the point (1,6,3) in the line ( frac{x}{1}=frac{y-1}{2}=frac{z-2}{3} ) has the
coordinates
A. (1,1,7)
в. (0,1,7)
c. (1,0,7)
D. None of these
7
40What is the order of rotational
symmetry of the given figure?
( A cdot 6 )
B. 4
( c cdot 8 )
D. None of these
7
41n the given figure, which of the
following is a line of symmetry?
A. Line A
B. Line B
c. Line
D. Non
7
42The number of lines of symmetry in a regular hexagon is
A . 4
B. 5
( c .6 )
D. 7
7
43The lines of symmetry in the double-
( A )
B. 1
( c )
( D )
7
44Divide the given shape in a Horizontal
symmetry (into 2 trapeziums)
(iii) into 2 trapeziums
7
45Write all the capital letters of the English alphabets which have two lines of symmetry.
( A cdot H, operatorname{land} x )
B. A,C and B
c. ( P, Q ) and ( R )
D. s,Y and z
7
46( triangle A B C ) is an isosceles triangle with
( A B=A C . ) Then the line of symmetry
for the ( triangle A B C ) will be:
This question has multiple correct options
A. Perpendicular bisector of ( B C )
B. Angle bisector of ( angle B )
C. Altitude from vertex ( A ) on line ( B C )
D. Median from vertex ( C ) to side ( A B )
7
47The number of capital letters of the English alphabets having both horizontal and vertical lines of
symmetry is –
A. 0
B.
( c cdot 4 )
D.
7
48State for ‘T’ true and ‘F’ for false.
(i) Number 0 has both rotational and
line of Symmetry.
(ii) A regular polygon of ( n ) sides has ( 2 n ) lines of symmetry.
(iii) A square has four lines of
symmetry and rotational symmetry of
order 2
(iv) A circle has finite number of lines of
symmetry.
(i) (ii) (iii) (iv)
( A cdot T F F F )
B. T F T F
c. F T F ( T )
D. F T T T
7
49Which figure below shows two quadrilaterals related by both rotational symmetry and line symmetry?
A. Figure
B. Figure i
C. Figure iii
D. None of these
7
50Find a transformation of the polygon
that does result in at least one type of
symmetry. Draw the image and list the coordinates of the vertices of the larger
shape. How do you know the diagram
has symmetry?
7
51Can you draw a triangle which has no lines of symmetry? Sketch a rough figure.7
52A line ( y=x ) is rotated through ( 60^{circ} )
Find the new angle made by line with ( x )
axis.
A . ( 105^{circ} )
B. ( 135^{circ} )
( mathbf{c} cdot 155^{circ} )
D. ( 120^{circ} )
7
53What is the order of rotational
7
54The diagram shows the outline of a 50
cent coin from Fiji

How many lines of symmetry does it
have?
A ( cdot 12 )
B.
( c )
( D )

7
55The number-of line symmetries that the
given square have:
( A )
( B )
( c )
( D )
7
56The number of lines of symmetry in a picture of Taj Mahal is – –
A.
B. 2
( c cdot 0 )
( D )
7
57If a scalene triangle is cut along its line of symmetry, then the number of triangles so formed is
A . 1
B. 2
( c .3 )
D. none of the above
7
58Can you draw a triangle which has exactly three lines of symmetry? Sketch a rough figure.7
59How many lines of symmetry are there for an isosceles triangle?
A . 1
B.
( c cdot 3 )
( D )
7
both line and rotational symmetry of
order more than 1
7
61Find the order of rotational symmetry of equilateral triangle.
A .2
B. 3
( c cdot 4 )
D.
7
62Draw, wherever possible, a rough sketch
of:

A triangle with both line and rotational symmetries of order more than 1

7
63What is the order of rotational
7
64The image of the point (3,-1,11) w.r.t
the line ( frac{boldsymbol{x}}{mathbf{2}}=frac{boldsymbol{y}-boldsymbol{2}}{boldsymbol{3}}=frac{boldsymbol{z}-boldsymbol{3}}{boldsymbol{4}} ) is
7
65Which square must be shaded so that
the figure has a line of symmetry?
begin{tabular}{|l|l|l|l|}
hline & & & \
hline & ( mathbf{R} ) & & \
hline & ( mathbf{P} ) & & ( mathbf{Q} ) \
hline & & & ( mathbf{S} ) \
hline
end{tabular}
( A cdot P )
в. ( Q )
( c . R )
D.
7
66The number of rotational symmetry of an equilateral triangle is/are:
A .
B.
( c cdot 3 )
( D )
7
67symmetry exists when the figure can be rotated and the image is identical to the original.
A. Rotational
B. Linear
c. Reflection
D. Non-linear
7
68Draw lines of symmetry for the following figures. Identify which of them have point symmetry. Is there any implication between lines of symmetry and point symmetry?7
69Where will the hand of a clock stop if it:
Start at 4 and makes ( frac{3}{4} ) of a revolution, clockwise?
7
70What do you face when we make an ( frac{3}{4} )
revolution anti-clockwise from west?
7
71topp
onwo
( ^{80^{circ}} )
7
72Can you draw a triangle having: three
lines of symmetry.
7
73Which figure shows the rotation image
of pentagon ( A ) after a ( 216^{circ} ) clockwise
A. Figure iii
B. Figure
c. Figure iv
D. Figure i
7
74The number of lines of symmetry for a rectangle is/are
A . 1
B. 2
( c .3 )
( D )
7
75The reflection of the point ( boldsymbol{P}(1,0,0) ) in the line ( frac{boldsymbol{x}-mathbf{1}}{mathbf{2}}=frac{boldsymbol{y}+mathbf{1}}{mathbf{- 3}}=frac{boldsymbol{z}+mathbf{1 0}}{mathbf{8}} ) is
A ( cdot(3,-4,-2) )
B ( cdot(5,-8,-4) )
c. (1,-1,-10)
D. (2,-3,8)
7
76The diagram shows the outline of a 50
cent coin from Fiji
What is its order of rotational
symmetry?
( A )
8.
( c cdot 12 )
D. 15
7
77A ( ——– ) has only one line of symmetry, two sets of equal sides and only one set of matching angles.7
78In the given figure, which of the
following is a line of symmetry?
A. Line A
B. Line B
c. Line
D. Line A and Line C
7
79The projection of the line ( x+y=0 )
( z=0 ) on the plane ( x-y+z=1 ) is
begin{tabular}{l}
A ( cdot frac{3 x-1}{3}=frac{3 y+1}{-3}=frac{3 z-1}{-2} ) \
hline
end{tabular}
B. ( frac{4 x-1}{3}=frac{2 y+1}{-3}=frac{4 z+1}{-6} )
begin{tabular}{l}
C. ( frac{3 x-1}{-3}=frac{3 y+1}{3}=frac{3 z-1}{6} ) \
hline
end{tabular}
D. ( frac{4 x-1}{2}=frac{2 y+1}{1}=frac{4 z+1}{-2} )
7
80The image of the point (1,6,3) in the ( operatorname{line} frac{x}{1}=frac{y-1}{2}=frac{z-2}{3} ) is
A. (1,0,7)
в. (1,3,5)
c. (2,4,6)
D. (-1,-6,-3)
7
81The image of the origin in the line joining the points (-9,4,5) and (11,0,-1) is
A. (2,4,4)
в. (1,2,2)
c. (1,2,3)
D. (2,2,1)
7
82On a squared paper, sketch the following: A triangle with a horizontal line of symmetry but no vertical line of
symmetry.
7
83Rectangle ABCD is the image of rectangle ABCD after which of the following rotations?
A . A ( 90^{circ} ) clockwise rotation about the origin
B. A ( 90^{circ} ) clockwise rotation about the point (1,1)
C. A ( 90^{circ} ) counterclockwise rotation about the point (1,1)
D. A ( 90^{circ} ) clockwise rotation about the point (2,1)
7
84A rectangle DEFG is plotted in ( X Y ) plane. The co-ordinates of D , E , F and G ( operatorname{are}(2,2),(9,2),(9,10) ) and (2,10)
Find the new co-ordinates of G when
DEFG is rotated ( 270^{circ} ) around origin. This question has multiple correct options
A ( cdot(-10,2) )
B. (10,-2)
c. (10,-1)
D. (10,2)
7
85What is the order of rotational symmetry
of the above pattern?
( A )
( B )
( c cdot 12 )
( D )
7
86What is the order of rotational
symmetry of the above pattern?
( A cdot 3 )
( B )
( c cdot 6 )
D. 12
7
87An equilateral triangle whose each side
is ( 4.5 mathrm{cm} . ) How many lines of symmetry
does it has????????
( A cdot 3 )
B. 2
( c )
D. infinite
7
88Which of the following is symmetrical about its diagonals?
A. Square
B. Rectangle
c. Parallelogram
D. None of these
7
89A line ( y=x ) is rotated through ( 45^{circ} )
Find the new angle made by line with ( x ) axis.
A ( cdot 90^{circ} )
B. ( 80^{circ} )
( c .75^{circ} )
D. None of these
7
90The number of lines of symmetry that
the given square has is
( A cdot 4 )
B. 2
( c cdot 3 )
D.
7
91A protractor has – symmetry.
A .
B. 2
( c .3 )
( D )
7
92How many of the alphabets have more
than 1 line of symmetry?
[
A B C D E F G H I J K L M N O
]
7
93How many lines of symmetry are there for an equilateral triangle.7
94John notices that a standard piece of
paper is a rectangle, how many lines of symmetry does it have?
( A )
B. 2
( c cdot 3 )
D. 4
7
95A figure has a rotational symmetry of order more than 1 , the angle of rotation
can be
A ( cdot 21^{circ} )
B . ( 22^{circ} )
( c cdot 23^{circ} )
D. ( 24^{circ} )
7
96The number of lines of symmetry in a regular pentagon is
A . 3
B. 4
( c .5 )
( D )
7
97A rectangle DEFG is plotted in ( X Y ) plane. The co-ordinates of D , E , F and G ( operatorname{are}(2,2),(9,2),(9,10) ) and (2,10)
Find the new co-ordinates of D when
DEFG is rotated ( 270^{circ} ) around origin.
A ( cdot(-2,-2) )
в. (2,-2)
c. (2,4)
(年. ( (2,4)) )
D. (-2,4)
7
98When a right triangle of area 3 is
rotated ( 360^{circ} ) about its shorter leg, the
solid that results has a volume of 30 Calculate the volume of the solid if
the same right triangle is rotated about
its longer leg.
A . 0.99
B. 7.90
c. 8.88
D. 31.42
E . 41.12
7
99Draw neat diagrams showing the line (or lines) of symmetry and give the specific name to the quadrilateral having: only one line of symmetry. How many quadrilaterals are there?7
100Which of the squares must be shaded
so that the dotted line AB becomes the
line of symmetry?
( A )
B. ( I I )
c. ( I I I )
D. ( I V )
7
101How many minimum squares must be
shaded to make the given figure
symmetric ?
( A )
B.
( c )
( D )
7
102This star is made up of equilateral
triangles: What is the order of rotational
symmetry of the star?
( A )
( B )
( c )
D. 12
7
103On squared paper copy the triangle in
the following figure. In a given case
draw the line (s) of symmetry if any
identify the type of the triangle.
7
104Write the number of lines of symmetry
in each letter ‘SYMMETRY’.
7
105The number of lines of symmetry in a
square is
A . 4
B. 3
( c cdot 2 )
D. Infinite
7
106What is the order of rotational
symmetry and angle of rotation symmetry for this design?
A ( cdot 4 ; 90^{circ} )
B. ( 6 ; 120^{circ} )
c. ( 8: 60^{circ} )
D . ( 8 ; 45^{circ} )
7
107Fill in the blanks.
Rotation turns an object about a ( P ) point. The fixed point is the centre of ( underline{Q} ) The angle by which the object rotates is the ( R )
Then, P Q R is:
A. fixed rotation angle of rotation
B. variable rotation central angle
c. fixed angle of rotation rotation
D. variable rotation angle of rotation
7
108What is the order of rotational
symmetry of this star?
( A )
3.4
( c )
( D )
7
109Assertion
The point ( boldsymbol{A}(mathbf{1}, mathbf{0}, mathbf{7}) ) is the mirror image of the point ( B(1,6,3) ) in the line ( : frac{x}{1}= ) ( frac{boldsymbol{y}-mathbf{1}}{mathbf{2}}=frac{boldsymbol{z}-mathbf{2}}{mathbf{3}} )
Reason
The line ( frac{x}{1}=frac{y-1}{2}=frac{z-2}{3} ) bisects
the line segment joining ( boldsymbol{A}(mathbf{1}, mathbf{0}, mathbf{7}) ) and ( boldsymbol{B}(mathbf{1}, mathbf{6}, mathbf{3}) )
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
7
110A rectangle has
A. Two lines of symmetry
B. Four lines of symmetry
C. Three lines of symmetry
D. None of these
7
111How many lines of symmetry does the
figure have?
A. 0
B. 1
( c cdot 2 )
( D )
7
112After rotating by ( 60^{circ} ) about a centre, a figure looks exactly the same as at its original position. At what other angle will this happen for the figure?
( mathbf{A} cdot 120^{circ} )
B. 100
( c cdot 150 )
D. ( 90^{circ} )
7
113A rectangle has
A. one line of symmetry
B. two lines of symmetry
C. three lines of symmetry
D. None of these
7
114This polygon is one-half of a shape. Use a vertical line through 5 on the ( x ) -axis as a line of symmetry to complete the shape by drawing its other half. Write the coordinates of the larger shape
formed by PQRS and its image.
7
115( = )7
116John notices that a standard piece of
paper is a rectangle ( ldots ) how many lines of symmetry does it have?
A . 1
B . 2
( c .3 )
D. 4
7
117If a rectangle has more than two lines of symmetry,then it must be a square.
A. True
B. False
7
118How many lines of symmetry are in this
isosceles triangle?
( A )
B. 2
( c cdot 3 )
( D )
7
119The angle of rotation symmetry for a shape is ( 60 . ) What is the order of
rotational symmetry?
( A cdot 6 )
B. 4
( c cdot 3 )
D. 8
7
120Find the image of the point (2,-1,5) in the line ( vec{r}=(11 hat{i}-2 hat{j}-8 hat{k})+ )
( lambda(10 hat{i}-4 hat{j}-1 hat{1} k) )
7
121Let, coordinates of the two points ( A & B ) be (1,2) and ( (7,5), ) respectively. The line
( A B ) is rotated through ( 45^{circ} ) in anticlockwise direction about the point of
trisection of ( mathrm{AB} ) which is nearer to B. The
equation of the line in the new position is
A. ( 2 x-y-6=0 )
в. ( x-y-1=0 )
c. ( 3 x-y-11=0 )
D. none of these
7
122Give the order the rotational symmetry
for each figure:
7
123A rectangle DEFG is plotted in ( X Y ) plane. The co-ordinates of D , E , F and G ( operatorname{are}(2,2),(9,2),(9,10) ) and (2,10)
Find the new co-ordinates of F when
DEFG is rotated ( 270^{circ} ) around origin.
This question has multiple correct options
A ( cdot(-10,9) )
B. (-10,-9)
c. (10,9)
D. (10,-9)
7
124Find the order of rotational symmetry
Refer above image.
7
125How many of the following letters have rotational symmetry of order more than
1?
( mathrm{R}, mathrm{B}, mathrm{F}, mathrm{H}, mathrm{O}, mathrm{P}, mathrm{S}, mathrm{W}, mathrm{X}, mathrm{Z}, mathrm{N} )
A .4
B. 9
( c .5 )
( D )
7

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