Use graph paper for this question (Take 2 cm = 1 unit along both x and y axis). A B C D is a quadrilateral whose vertices are A 2 , 2 , B 2 , - 2 , C 0 , - 1 and D 0 , 1 . Write down the coordinates of A ' and B ' when reflected in the y -axis.

Given, ABCD is a quadrilateral whose vertices are A(2,2), B(2,-2), C(0,-1) , and D(0,1) . We need to find the coordinates of point A' and B' when reflected in the y -axis. We know that when you reflect a point across the x -axis, the x - coordinate remains the same, but the y -coordinate is transformed into its opposite (its sign is changed). Also, when you reflect a point across the y -axis, the y - coordinate remains the same, but the x -coordinate is transformed into its opposite (its sign is changed). Hence, if we reflect point A and point B in y -axis, we get, the coordinates of A'= - 2 , 2 and B'= - 2 , - 2 .

Use a graph sheet for this question. Take 1 c m = 1 unit along both x and y -axis. Plot the following points: A ( 0 , 5 ) , B ( 3 , 0 ) , C ( 1 , 0 ) and D ( 1 , – 5 ) . Reflect the points B , C and D on the y -axis and name them as B ' , C ' and D ' respectively. Write down the coordinates of B ' , C ' and D ' .

According to the question, Take 1 cm = 1 unit along both x and y -axis. A ( 0 , 5 ) , B ( 3 , 0 ) , C ( 1 , 0 ) and D ( 1 , – 5 ) We know that, when you reflect a point across the y -axis, the y -coordinate remains the same, but the x -coordinate is taken to be the additive inverse. The reflection of point x , y across the y -axis is - x , y . Therefore, the points B , C and D are reflected on the y -axis and the coordinates of B ' , C ' and D ' are B ' ( - 3 , 0 ) , C ' ( - 1 , 0 ) and D ' ( - 1 , – 5 ) .

Use a graph sheet for this question. Take 1 cm = 1 unit along both x and y axis. Some points are A 0 , 5 , B 3 , 0 , C 1 , 0 and D 1 , - 5 . The reflection of the points B , C and D on y - axis are B ' , C ' and D ' . Join the points A , B , C , D , D ' , C ' , B ' A in order and give a name to the closed figure A B C D D ' C ' B ' .

Given, 1 cm = 1 unit on the graph paper. The points are A 0 , 5 , B 3 , 0 , C 1 , 0 and D 1 , - 5 . We know that, when you reflect a point across the y -axis, the y -coordinate remains the same, but the x -coordinate is taken to be the additive inverse. The reflection of point x , y across the y -axis is - x , y . Thus, the reflected points of B , C , D on y - axis are B ' - 3 , 0 , C ' - 1 , 0 and D ' - 1 , - 5 . The points are plotted on the graph paper and A , B , C , D , D ' , C ' , B ' , A are joined. The closed figure is an arrow head.

Use a graph sheet for this question. Take 1 cm = 1 unit along both x and y -axis. A ( 0 , 5 ) , B ( 3 , 0 ) , C ( 1 , 0 ) and D ( 1 , – 5 ) Reflect the points B , C and D on the y -axis and name them as B ' , C ' and D ' respectively.

According to the question, Take 1 cm = 1 unit along both x and y -axis. A ( 0 , 5 ) , B ( 3 , 0 ) , C ( 1 , 0 ) and D ( 1 , – 5 ) We know that, when you reflect a point across the y -axis, the y -coordinate remains the same, but the x -coordinate is taken to be the additive inverse. The reflection of point x , y across the y -axis is - x , y . Therefore, reflect the points B , C and D on the y -axis are B ' ( - 3 , 0 ) , C ' ( - 1 , 0 ) and D ' ( - 1 , – 5 )

Use graph paper for this question. (Take 2 cm = 1 unit along both x - and y -axis). ABCD is a quadrilateral whose vertices are A 2 , 2 , B 2 , - 2 , C 0 , - 1 and D 0 , 1 . Name two points which are invariant in the reflection on y -axis.

Given, ABCD is a quadrilateral whose vertices are A(2,2), B(2,-2), C(0,-1) , and D(0,1) . We know that when you reflect a point across the x -axis, the x - coordinate remains the same, but the y -coordinate is transformed into its opposite (its sign is changed). Also, when you reflect a point across the y -axis, the y - coordinate remains the same, but the x -coordinate is transformed into its opposite (its sign is changed). A point is called an invariant point with respect to a given line if and only if it lies on the line. This means the coordinate of a point does not change on reflection in the line. Hence, if we reflect point A and point B in y -axis, then, we obtain, the coordinates of A'= - 2 , 2 , B'= - 2 , - 2 . The coordinates of C 0 , - 1 and D 0 , 1 remain the same on reflection in the y -axis because they remain invariant points on reflection in the y -axis.

Use graph paper for this question. (Take 2 cm = 1 unit along both x - and y -axis). ABCD is a quadrilateral whose vertices are A 2 , 2 , B 2 , - 2 , C 0 , - 1 and D 0 , 1 . Reflect the quadrilateral A ' B ' C D in the y -axis and name the polygon A ' B ' CD .

Given, ABCD is a quadrilateral whose vertices are A(2,2), B(2,-2), C(0,-1) , and D(0,1) . We know that when you reflect a point across the x -axis, the x - coordinate remains the same, but the y -coordinate is transformed into its opposite (its sign is changed). Also, when you reflect a point across the y -axis, the y - coordinate remains the same, but the x -coordinate is transformed into its opposite (its sign is changed). Hence, if we reflect point A and point B in y -axis, then, we obtain, the coordinates of A'= - 2 , 2 , B'= - 2 , - 2 . The coordinates of C 0 , - 1 and D 0 , 1 remain the same on reflection in the y -axis because they remain invariant points on reflection in the y -axis. The reflected quadrilateral A ' B ' C D is shown below. Here, A ' B ' is parallel to the y -axis. Hence, clearly, the figure A ' B ' CD is a trapezium.

Use graph paper for this question. (Take 2 cm = 1 unit along both x - and y -axis). ABCD is a quadrilateral whose vertices are A 2 , 2 , B 2 , - 2 , C 0 , - 1 and D 0 , 1 . Reflect quadrilateral ABCD on the y -axis and name it as A ' B ' CD .

Given, ABCD is a quadrilateral whose vertices are A(2,2), B(2,-2), C(0,-1) , and D(0,1) . We know that when you reflect a point across the x -axis, the x - coordinate remains the same, but the y -coordinate is transformed into its opposite (its sign is changed). Also, when you reflect a point across the y -axis, the y - coordinate remains the same, but the x -coordinate is transformed into its opposite (its sign is changed). Hence, if we reflect point A and point B in y -axis, then, we obtain, the coordinates of A'= - 2 , 2 , B'= - 2 , - 2 . The coordinates of C 0 , - 1 and D 0 , 1 remain the same on reflection in the y -axis because they remain invariant points on reflection in the y -axis. The reflected quadrilateral A ' B ' C D is shown below.

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The reflection of the point $A (4, - 1)$ in the line $x = 2$ is

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Important Questions on Reflection

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IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 10 - Reflection>Multiple Choice Questions>Q 6

The reflection of the point

(- 3, 0)

in the origin is the point

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Understanding ICSE Mathematics Class 10>Chapter 10 - Reflection>Multiple Choice Questions>Q 7

Which of the following points is invariant with respect to the line

y = - 2

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Understanding ICSE Mathematics Class 10>Chapter 10 - Reflection>Chapter Test>Q 1

The point

P (4, - 7)

on reflection in

x

-axis is mapped onto

P'

. Then

P'

on reflection in the

y

-axis is mapped onto

P''

. Find the coordinates of

P'

and

P''

. Write down a single transformation that maps

P

onto

P''

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Understanding ICSE Mathematics Class 10>Chapter 10 - Reflection>Chapter Test>Q 2

The point

P (a, b)

is first reflected in the origin and then reflected in the

y

axis to

P'

. If

P'

has coordinates

(3, - 4)

, evaluate

a, b

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Understanding ICSE Mathematics Class 10>Chapter 10 - Reflection>Chapter Test>Q 3

A point

P (a, b)

becomes

(- 2, c)

after reflection in the

x

-axis, and

P

becomes

(d, 5)

after reflection in the origin. Find the values of

a, b, c

and

d

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Understanding ICSE Mathematics Class 10>Chapter 10 - Reflection>Chapter Test>Q 4

A (4, - 1), B (0, 7)

and

C (- 2, 5)

are the vertices of a triangle.

△ A B C

is reflected in the

y

-axis and then reflected in the origin. Find the coordinates of the final images of the vertices.

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Understanding ICSE Mathematics Class 10>Chapter 10 - Reflection>Chapter Test>Q 5

The points

A (4, - 11), B (5, 3), C (- 2, 5)

and

D (1, 1)

are the vertices of a parallelogram. If the parallelogram is reflected in the

y

-axis and then in the origin, find the coordinates of the final images. Check whether it remains a parallelogram. Write down a single transformation that brings the above change.

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IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 10 - Reflection>Chapter Test>Q 6

Use a graph paper for this question (take $2 cm = 1$ unit on both $x$ and $y$ axes).

$(i)$ Plot the following points: $A (0, 4), B (2, 3), C (1, 1)$ and $D (2, 0)$ .

$(i i)$ Reflect points $B, C, D$ on $y$ -axis and write down their coordinates. Name the images as $B', C', D'$ respectively.

$(i i i)$ Join points $A, B, C, D, D', C', B'$ and $A$ in order, so as to form a closed figure. Write down the equation of line of symmetry of the figure formed.

The reflection of the point A4, -1 in the line x=2 is

Important Questions on Reflection

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The reflection of the point $A (4, - 1)$ in the line $x = 2$ is