ML Aggarwal Solution Class 10 Chapter 10 Reflection Test

 Test

Question 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 co-ordinates of P’ and P”. Write down a single transformation that maps P onto P”.

Sol :

P’ is the image of P (4, -7) reflected in x-axis

∴ Co-ordinates of P’ are (4, 7)

Again P” is the image of P’ reflected in y-axis

∴ Co-ordinates of P” are (-4, 7)

∴ Single transformation that maps P and P” is in the origin.


Question 2

The point P (a, b) is first reflected in the origin and then reflected in the y-axis to P’. If P’ has co-ordinates (3, – 4), evaluate a, b

Sol :

The co-ordinates of image of P(a, b) reflected in origin are (-a, -b).

Again the co-ordinates of P’, image of the above point (-a, -b)

reflected in the y-axis are (a, -b).

But co-ordinates of P’ are (3, -4)

∴a = 3 and -b = -4

b = 4 Hence a = 3, b = 4.


Question 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.

Sol :

If the image of P (a, b) after reflected in the x-axis be (a, -b) but it Is given (-2, c).

a = -2, c = -b

If P is reflected in the origin, then its co-ordinates will be (-a, -b), but it is given (d, 5)

∴ -b = 5 ⇒ b = -5

d = -a = -(-2) = 2, c = -b = -(-5) = 5

Hence a = -2, b = -5, c = 5, d = 2


Question 4

A (4, – 1), B (0, 7) and C ( – 2, 5) are the vertices of a triangle. ∆ ABC is reflected in the y-axis and then reflected in the origin. Find the co-ordinates of the final images of the vertices.

Sol :

A (4, -1), B (0, 7) and C (-2, 5) are the vertices of ∆ABC.

After reflecting in y-axis, the co-ordinates of points will be

A’ (-4, -1), B’ (0, 7), C’ (2, 5). Again reflecting in origin,

the co-ordinates of the images of the vertices will be

A” (4, 1), B” (0, -7), C” (-2, -5)


Question 5

The points A (4, – 11), B (5, 3), C (2, 15), 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 co-ordinates of the final images. Check whether it remains a parallelogram. Write down a single transformation that brings the above change.

Sol :

The points A (4, -11), B (5, 3), C (2, 15) and D (1, 1) are the vertices of a parallelogram.

After reflecting in/-axis, the images of these points will be

A’ ( -4, 11), B’ (-5, 3), C (-2, 15) and D’ (-1, 1).

Again reflecting these points in origin, the image of these points will be

A” (4, -11), B” (5, -3), C” (2, -15), D” (0, -1)

Yes, the reflection of a single transformation is in the x-axis.


Question 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).

(ii) Reflect points B, C, D on 7-axis and write down their coordinates. Name the images as B’, C’, D’ respectively.

(iii) 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. (2017)

Sol :

(i) On graph A (0, 4), B (2, 3), C (1, 1) and D (2, 0)

(ii) B’ = (-2, 3), C’ = (-1, 1), D’ = (-2, 0)

















Question 7

The triangle OAB is reflected in the origin O to triangle OA’B’. A’ and B’ have coordinates ( – 3, – 4) and (0, – 5) respectively.
(i) Find the co-ordinates of A and B.
(ii) Draw a diagram to represent the given information.
(iii) What kind of figure is the quadrilateral ABA’B’?
(iv) Find the coordinates of A”, the reflection of A in the origin followed by reflection in the y-axis.
(v) Find the co-ordinates of B”, the reflection of B in the x-axis followed by reflection in the origin.
Sol :
∆ OAB is reflected in the origin O to ∆ OA’B’,
Co-ordinates of A’ = (-3, -4), B’ (0, -5).
.’. Co-ordinates of A will be (3, 4) and of B will be (0, 5).
(ii) The diagram representing the given information has been drawn here.
(iii) The figure in the diagram is a rectangle.
(iv) The co-ordinates of B’, the reflection of B is the x-axis is (0, -5)
and co-ordinates of B”, the reflection in origin of the point (0, -5) will be (0, 5).
(v) The co-ordinates of the points, the reflection of A in the origin are (-3, -4)
and coordinates of A”, the reflected in y-axis of the point (-3, – 4) are (3, -4)


 

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