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Byju's Answer

Standard X

Mathematics

Reflection

Use graph pap...

Question

Use graph paper and taking $1 c m = 1 u n i t$ along with $x - a x i s$ and $y - a x i s$
Plot the point $A (- 4, 4)$ and $B (2, 2)$
Reflect $A$ and $B$ in the origin to get the image $A'$ and $B'$ respectively.
Write the coordinates of $A'$ and $B'$
Give the geometric name for the figure $A B A' B'$

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Solution

Step 1: Plotting the points on graph
On plotting the given points $A (- 4, 4)$ and $B (2, 2)$ we get :

Step 2: Reflecting A and B in origin
We know that, reflection of a point $(x, y)$ in the origin is given by $(- x, - y)$
Therefore, reflection of $A (- 4, 4)$ in the origin is given by $A' (4, - 4)$
Reflection of $B (2, 2)$ in the origin is given by $B' (- 2, - 2)$
The images reflected can be seen also in the graph.
Step 3: Coordinates of $A'$ and $B'$
The coordinates of image $A' (4, - 4)$
The coordinate of image $B' (- 2, - 2)$
Step 4: Naming the figure $A B A' B'$
From the graph we can clearly see that the figure $A B A' B'$ is a rhombus.
Hence, $A' (4, - 4)$ , $B' (- 2, - 2)$ are found and the figure $A B A' B'$ is a rhombus.

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Similar questions

(i) Plot the points A (3, 5) and B (-2, -4). Use 1 cm = 1 unit on both the axes.

(ii) A' is the image of A when reflected in the x-axis. Write down the co-ordinates of A' and plot it on the graph paper.

(iii) B' is the image of B when reflected in the y-axis, followed by reflection in the origin. Write down the co-ordinates of B' and plot it on the graph paper.

(iv) Write down the geometrical name of the figure AA'BB'.

(v) Name two invariant points under reflection in the x-axis.

Attempt this question on graph paper.

(a) Plot A (3, 2) and B (5, 4) on graph paper.

(b) Reflect A and B in the x-axis to A' and B' respectively. Plot these points also on the same graph paper.

(i) the geometrical name of the figure ABB' A';

(ii) the measure of angle ABB';

(iii) the image A" of A, when A is reflected in the origin.

(iv) the single transformation that maps A' to A".

Q. Using graph paper and taking

1 c m = 1

unit along both

x

-axis and

y

-axis.
(i) Plot the points

A (- 4, 4)

and

B (2, 2)

(ii) Reflect

A

and

B

in the origin to get images

A^{'}

and

B^{'}

respectively.
(iii) Write down the co-ordinates of

A^{'}

and

B^{'}

.
(iv) Give the geometrical name for the figure

A B A^{'} B^{'}

(v) Draw and name its lines of symmetry.

Q. Using graph paper, (take

2 c m = 1

unit on both axis), plot

A (- 4, 2)

and

B (2, 4)

A^{'}

is the image of

A

when reflected in the

y

-axis. Plot it on the graph paper and write the coordinates of

A^{'}

B^{'}

is the image of

B

when reflected about the line

A A^{'}

. Join

A - B - A^{'} - B^{'}

and name the quadrilateral.

Q. Use a graph paper for this question taking

1 c m = 1

unit along both the

x

and

y

axis :
(i) Plot the points

A (0, 5), B (2, 5), C (5, 2), D (5, - 2), E (2, - 5)

and

F (0, - 5)

(ii) Reflect the points

B, C, D

and

E

on the

y

-axis and name them respectively as

B^{'}, C^{'}, D^{'}

and

E^{'}

.
(iii) Write the coordinates of

B^{'}, C^{'}, D^{'}

and

E^{'}

.
(iv) Name the figure formed by

B C D E E^{'} D^{'} C^{'} B^{'}

.
(v) Name a line of symmetry for the figure formed.

Join BYJU'S Learning Program

Use graph paper and taking 1cm=1unit along with x-axis and y-axisPlot the point A(-4,4) and B(2,2)Reflect A andB in the origin to get the image A' and B'respectively.Write the coordinates of A'andB'Give the geometric name for the figure ABA'B'