# ML Aggarwal Solutions for Chapter 10 Reflection Class 10 Maths ICSE

**Exercise 10.1**

**1. Find the co-ordinates of the images of the following points under reflection in the x-axis:**

**(i) (2, -5) **

**(ii) (–3/2, -1/2)**

**(iii) (-7, 0) **

**Answer**

Co-ordinates of the images of the points under reflection in the x-axis will be

(i) Image of (2, -5) will be (2, 5)

(ii) Image of (-3/2, -1/2) will be (-3/2, 1/2)

(iii) Image of (-7, 0) will be (-7, 0)

**2. Find the co-ordinates of the images of the following points under reflection in the y-axis: **

**(i) (2, -5) **

**(ii) – 3/2, 1/2**

**(iii) (0, - 7) **

**Answer**

Co – ordinates of the image of the points under reflection in the y- axis

(i) Image of (2, - 5) will be (-2, 5)

(ii) Image of -3/2, 1/2 will be 3/2, 1/2

(iii) Image of (0, -7) will be (0, -7)

**3. Find co-ordinates of the images of the following points under reflection in the origin. **

**(i) (2, -5) **

**(ii) (-3/2, -1/2)**

**(iii) (0, 0) **

**Answer**

Co-ordinates of the image of the points under reflection in the y-axis

(i) Image of (2, -5) will be (-2, 5)

(ii) Image of -3/2, -1/2 will be 3/2, 1/2

(iii) Image of (0, 0) will be (0, 0)

**4. The image of a point P under reflection in the x-axis is (5, -2). **

**Write down the co-ordinates of P. **

**Answer**

As the image of a point (5, -2) under x-axis is P

∴ Co-ordinates of P will be (5, 2)

**5. A point P is reflected in the x-axis. Co-ordinates of its image are (8, -6). **

**(i) Find the co-ordinates of P. **

**(iii) Find the co-ordinates of the image of P under reflection in the y-axis. **

**Answer**

The co-ordinates of image of P which is reflected in x-axis are (8, -6), then

**(i)** Co-ordinates of P will be (8, 6)

**(ii)** Co-ordinates of image P under reflection in the y-axis will be (-8, 6)

**6. A point P is reflected in the origin. Co-ordinates of its image are (2, -5). Find **

**(i) the co-ordinates of P. **

**(ii) The co-ordinates of the image of P in the x- axis. **

**Answer**

The co-ordinates of image of a point P which is reflected in origin are (2, -5), then

**(i)** Co-ordinates of P will be (-2, 5)

**(ii)** Co-ordinates of the image of P in the x-axis will be (-2, - 5)

**7. (i) The point P (2, 3) is reflected in the line x = 4 to the point P’. Find the co-ordinates of the point P’. **

**(ii) Find the image of the point P (1, - 2) in the line x = - 1.**

**Answer**

**(i) **(a) Draw axis XOX’ and YOY’ and take 1 cm = 1 unit

(b) Plot point P (2, 3) on it.

(c) Draw a line x = 4 which is parallel to y-axis.

(d) From P, draw a perpendicular on x = 4, which intersects x = 4 at Q.

(e) Produce PQ to P’ such that QP’ = QP.

∴ P’ is the reflection of P in the x = 4

Co-ordinates of P’ are (6, 3)

**(ii)** (a) Draw axis XOX’ and YOY’ and take 1 cm = 1 unit.

(b) Plot the point P(1, -2) on it.

(c) Draw a line x = - 1 which is parallel to y-axis.

(d) From p, draw a perpendicular on the line x = -1, which meets it at Q.

(e) Produce PQ to P’ such that PQ = QP’

P’ is the image or reflection of P in the line x = - 1

Co-ordinates of P’ are (-3, -2)

Co –ordinates of P’ are (-3, - 2)

**8.(i) The point P (2, 4) on reflection in the line y = 1 is mapped onto P’. Find the co-ordinates of P’. **

**(ii) Find the image of the point P (-3, -5) in the line y = - 2. **

**Answer**

**(i)** (a) Draw axis XOX’ and YOY’ and take 1 cm = 1 unit.

(b) Plot point P (2, 4) on it.

(c) Draw a line y = 1 which is parallel to the x-axis.

(d) From P, draw a perpendicular on y = 1 which meets it at Q.

(e) Produce PQ to P’ such that QP’ = PQ.

P’ is the image of P, whose co-ordinates are (2, -2)

**(ii)** (a) Draw axis XOX’ and YOY’ and take 1 cm = 1 unit.

(b) Plot point P (-3, -5) on it.

(c) Draw a line y = - 2 which is parallel to the x-axis.

(d) From P, draw a perpendicular on y = - 2 which meets it at Q.

(e) Produce PQ to P’ such that QP’ = PQ.

Then P’ is the image of P, whose co-ordinates are (-3, 1)

**9.** **The point (-4, -5) on reflection in y-axis is mapped on P’. The point P’ on reflection in the origin is mapped on P’’. Find the co-ordinates of P’ and P’’. Write down a single transformation that maps P onto P’’.**

**Answer**

P’ is the image of point P (-4, -5) in y-axis

∴ Co-ordinates of P’ will be (4, -5)

Again P’’ is the image of P’ under reflection in origin will be (-4, 5).

The single transformation that maps P onto P’’ is the x-axis.

**10. Write down the co-ordinates of the image of the point (3, -2) when : **

**(i) reflected in the x-axis**

**(ii) reflected in the y-axis **

**(iii) reflected in the x-axis followed by reflection in the y-axis. **

**(iv) reflected in the origin. **

**Answer**

Co-ordinates of the given points are (3, -2).

(i) Co-ordinates of the image reflected in y – axis will be (3, 2)

(ii) Co-ordinates of the image reflected in y-axis will be (-3, -2)

(iii) Co-ordinates of the point reflected in x- axis followed by reflection in the y-axis will be (-3, 2).

(iv) Co-ordinates of the point reflected in the origin will be (-3, 2)

**11. Find the co-ordinates of the image of (3, 1) under reflection in x-axis followed by a reflection in the line x = - 1. **

**Answer**

(i) Draw axis XOX’ and YOY’ taking 1 cm = 1 unit.

(ii) Plot a point P (3, 1)

(iii) Draw a line x = 1, which is parallel to y-axis.

(iv) From P, draw a perpendicular on x-axis meeting it at Q.

(v) Produce PQ to P’ such that QP’ = PQ, then

P’ is the image of P is x-axis. Then co-ordinates of P’ will be (3, - 1)

(vi) From P’, draw a perpendicular on x = 1 meeting it at R.

(vii) Produce P’R to P’’ such that RP’’ = P’R

∴ P’’ is the image of P’ in the line x = 1

Co- ordinates of P’’ are (-1, -1)

**12. If P’ (-4, - 3) is the image of a point P under refection in the origin, find**

**(i) the co-ordinates of P. **

**(ii) the co-ordinates of the image of P under reflection in the line y = - 2. **

**Answer**

**(i)** Reflection of P is P’ (- 4, -3) in the origin

∴ Co-ordinates of P will be (4, 3)

Draw a line y = - 2, which is parallel to x- axis.

**(ii)** From P, draw a perpendicular on y = - 2 meetings it at Q

Produce PQ to P’’ such that QP’’ = PQ

∴ P’’ will the image of P in the line y = - 2

∴ Co-ordinates of P’’ will be (4, -7)

**13. A point P (a, b) is reflected in the x- axis to P’ (2, -3), write down the values of a and b. P’’ is the image of P, when reflected in the y-axis. Write down the co-ordinates of P’’. Find the co-ordinates of P’’, when P is reflected in the line parallel to y-axis such that x = 4.**

**Answer**

P’ (2, -3) is the reflection of P (a, b) in the x-axis

∴ Co –ordinates of P’ will be (a, - b) but P’ is (2, -3)

Comparing a = 2, b = 3

∴ Co –ordinates of P will be (2, 3)

P’’ is the image of P when reflected in y-axis

∴ Co-ordinate of P’’ will be (-2, 3)

Draw a line x = 4, which is parallel to y-axis

And P’’ is the image of P when it is reflected in the line x = 4,

Then P’’ is its reflection Co-ordinates of P’’ will be (6, 3).

**14. (i) Point P (a, b) is reflected in the x-axis to P’ (5, -2). Write down the values of and b. **

**(ii) P’’ is the image of P when reflected in the y-axis. Write down the co-ordinates of P’’.**

**(iii) Name a single transformation that maps P’ to P’’. **

**Answer**

**(i) **Image of P (a, b) reflected in the x-axis to P’ (5, -2)

∴ a = 5 and b = 2

**(ii)** P’’ is the image of P when reflected in the y-axis

∴ Its co-ordinates will be (-5, -2).

**(iii)** The single transformation that maps P’ to P’’ is the origin.

**15. Points A and B have co-ordinates (2, 5) and (0, 3). Find **

**(i) the image A’ of A under reflection in the x-axis. **

**(ii) the image B’ of B under reflection in the line AA’.**

**Answer**

Co-ordinates of A are (2, 5) and of B are (0, 3)

**(i)** Co-ordinates of A’, the image of A reflected in the x- axis will be (2, -5)

**(ii)** Co-ordinates of B’, the image of B under reflection in the line AA’ will be (4, 3).

**16. Plot the points A(2, -3), B (- 1, 2) and C (0, -2) on the graph paper. Draw the triangle formed by reflecting these points in the x-axis. Are the two triangles congruent ? **

**Answer**

The points A (2, -3), B (-1, 2) and C (0, -2) has been plotted on the graph paper as shown and are joined to form a triangle ABC. The co-ordinates of the images of A, B and C reflected in x-axis will be A’ (2, 3), B’ (-1, -2), C’ (0, 2) respectively and are joined to from another ∆A’B’C’

Yes, these two triangles are congruent.

**17. The points (6, 2), (3, -1) and (-2, 4) are the vertices of a right angled triangle. Check whether it remains a right angled triangle after reflection in the y-axis. **

**Answer**

Let A (6, 2), B (3, -1) and C (-2, 4) be the points of a right-angled triangle then the co-ordinates of the images of A, B, C reflected in y-axis be

A’ (-6, 2), B’ (- 3, -1) and C’ (2, 4)

**18. The triangle ABC where A (1, 2), B (4, 8), C (6, 8) is reflected in the x-axis to triangle A’ B’ C’. The triangle A’ B’ C’ is then reflected in the origin to triangle A” B” C”. Write down the co-ordinates of A”, B”, C”. Write down a single transformation that maps ABC onto A” B’’ C’’. **

**Answer**

The co-ordinates of ∆ABC are A (1, 2) B (4, 8), C (6, 8) which are reflected in x-axis as A’ B’ and C’.

∴ The co-ordinates of A’ (1, -2), B (4, -8) and C (6, - 8).

A’, B’ and C’ are again reflected in origins to form an ∆A’’B’’C’’.

∴ The co-ordinates of A’’ will be (-1, 2), B’’(-4, 8) and C’’(-6, 8)

The single transformation that maps ABC onto A’’ B’’ C’’ is y-axis.

**19. The image of a point P on reflection in a line l is point P’. Describe the location of the line l. **

**Answer**

The line will be the right bisector of the line segment joining P and P’.

**20. Given two points P and Q, and that (1) the image of P on reflection in y-axis is the point Q and (2) the mid-point of PQ is invariant on reflection in x-axis. Locate **

**(i) the x-axis **

**(ii) the y- axis and **

**(iii) the origin. **

**Answer**

Q is the image of P on reflection in y- axis.

And mid point of PQ is invariant on reflection in x-axis.

(i) x- axis will be the line joining the points P and Q.

(ii) The line perpendicular bisector of line segment PQ is the y-axis.

(iii) The origin will be the mid point of line segment PQ.

**21. The point (-3, 0) on reflection in a line is mapped as (3, 0) and the point (2, -3) on reflection in the same line is mapped as (-2, -3). **

**(i) Name the mirror line. **

**(ii) Write the co-ordinates of the image of (-3, - 4) in the mirror line. **

**Answer**

The point (-3, 0) is the image of point (3, 0)

And point (2, -3) is image of point (-2, -3) reflected on the same line.

(i) It is clear that the mirror line will be y- axis.

(ii) The co-ordinates of the image of the point (-3, -4)

Reflected in the same line i.e., y-axis will be (3, -4).

**22. Use graph paper for this (take 2 cm = 1 unit long 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).**

**(i) Reflect quadrilateral ABCD on the y-axis and name it as A’B’CD. **

**(ii) Write down the coordinates of A’ and B’. **

**(iii) Name two points which are invariant under the above reflection. **

**(iv) Name the polygon A’B’CD.**

**Answer:**

**(i)** Quadrilateral ABCD is reflected on the y-axis and named as A’B’CD.

**(ii)** As A’ is the refection of A (2, 2) about the line x = 0 (y-axis)

Thus, the coordinate of A’ are (-2, 2).

And, as B’ is the reflection of B are (-2, -2).

**(iii)** Points C (0, 1) and D (0, 1) are invariant under the above reflection.

**(iv)** The polygon A’B’CD is a trapezium since A’B’ || CD.

**23. Use graph paper for this question. **

**(i) The point P (2, -4) is reflected about the line x = 0 to get the image Q. Find the co-ordinates of Q. **

**(ii) Point Q is reflected about the line y = 0 to get the image R. Find the co-ordinates of R. **

**(iii) Name the figure PQR. **

**(iv) Find the area of figure PQR. **

**Answer**

**(i)** Since the point Q is the reflection of the point P (2, -4) in the line x = 0, the co-ordinates of Q are (2, 4).

**(ii)** Since R is the reflection of Q (2, 4) about the line y = 0, the co-ordinates of R are (-2, 4).

**(iii)** Figure PQR is the right angled triangle PQR.

**(iv)** Area of ∆PQR = 1/2 × QR × PQ

= 1/2 × 4 × 8

= 16 sq. units.

**24. Use graph paper for this question. The point P (5, 3) was reflected in the origin to get the image P’. **

**(i) Write down the co-ordinates of P’. **

**(ii) If M is the foot of perpendicular from P to the x-axis, find the co-ordinates of M. **

** (iii) If N is the foot of the perpendicular from P’ to the x-axis, find the co-ordinates of N. **

**(iv) Name the figure PMP’N. **

**(v) Find the area of the figure PMP’N. **

**Answer**

P’ is the image of point P (5, 3) reflected in the origin.

**(i) **Co-ordinates of P’ will be (-5, -3).

**(ii)** M is the foot of the perpendicular from P to the x-axis. Co-ordinates of M will be (5, 0)

**(iii) **N is the foot of the perpendicular from P’ to x-axis. Co-ordinates of N will be (-5, 0).

**(iv)** By joining the points, the figure PMP’N is a parallelogram.

**(v)** Area of the parallelogram = 2 × Area of ∆ MPN

= 2 × 1/2 × MN × PM

= MN × PM

= 10 × 3

= 30 sq. units.

**25. Using a graph paper, plot the points A (6, 4) and B (0, 4). **

**(i) Reflect A and B in the origin to get the images A’ and B’. **

**(ii) Write the co-ordinates of A’ and B’.**

**(iii) State the geometrical name for the figure ABA’B’. **

**(iv) Find its perimeter. **

**Answer**

(i) A (6, 4), B (0, 4)

(ii)

(iv)

Perimeter = Sum of all sides = 6 + 10 + 6 + 10 = 32 units

**26. Use graph paper to answer this question. **

**(i) Plot the points A (4, 6) and B (1, 2)**

**(ii) If A’ is the image of A when reflected in x- axis, write co-ordinates of A’. **

**(iii) If B’ is the image of B when B is reflected in the line AA’. Write the co-ordinates of B’. **

**(iv) Give the geometrical name for the figure ABA’B’. **

**Answer**

(i) Plotting the points A (4, 6) and B (1, 2) on the given graph.

(ii) A’ = (4, -6)

(iii) B’ = (7, 2)

(iv) In the quadrilateral ABA’B’, we have AB = AB’ and A’B = A’B’

Hence, ABA’B’ is a kite.

**27. The points A (2, 3), B (4, 5) and C (7, 2) are the vertices of ****∆****ABC. **

**(i) Write down the co-ordinates of A _{1}, B_{1}, C_{1} if **

**∆**

**A**

_{1}B_{1}C_{1 }is the image of**∆**

**ABC when reflected in the origin.**

**(ii) Write down the co-ordinates of A _{2}, B_{2}, C_{2 }if **

**∆**

**A**

_{2}B_{2}C_{2}is the image of**∆**

**ABC when reflected in the x-axis.**

**(iii) Assign the special name to the quadrilateral BCC _{2}B_{2 }and find its area. **

**Answer**

Points A (2, 3), B (4, 5) and C (7, 2) are the vertices of ∆ABC.

A_{1}, B_{1} and C_{1} are the images of A, B and C reflected in the origin.

**(i)** Co-ordinates of A_{1} = (-2, -3) of B_{1} (-4, -5) and of C_{1 }(-7, -2).

**(ii)** Co-ordinates of A_{2}, B_{2} and C_{2 }the images of A, B and C when reflected in x-axis are A_{2} (2, -3), B_{2} (4, -5), C_{2} (7, -2)

**(iii)**The quadrilateral formed by joining the points, BCC

_{2}B

_{2}is an isosceles trapezium and its area

= 1/2(BB_{2} + CC_{2}) ×3

= 1/2(10 + 4) × 3

= 1/2 × 14 × 3

= 21 sq. units.

**28. The point P (3, 4) is reflected to P’ in the x-axis and O’ is the image of O (origin) in the line PP’. Find :**

**(i) the co-ordinates of P’ and O’, **

**(ii) the length of segments PP’ and OO’.**

**(iii) the perimeter of the quadrilateral POP’O’. **

**Answer**

P’ is the image of P (3, 4) reflected in x- axis. And O’ is the image of O the origin in the line P’P.

**(i)** Co-ordinates of P’ are (3, -4) and co-ordinates of O’ reflected in PP’ are (6, 0)

**(ii)** Length of PP’ = 8 units and OO’ = 6 units

**(iii)** Perimeter of POP’O’ is

4 × OP

**29. Use a graph for this question. (Take 10 small divisions = 1 unit on both axes). P and Q have co-ordinates (0, 5) and (-2, 4).**

**(i) P is invariant when reflected in an axis. Name the axis. **

**(ii) Find the image of Q on reflection in the axis found in (i). **

**(iii) (0, k) on reflection in the origin is invariant. Write the value of k. **

**(iv) Write the co-ordinates of the image of Q, obtained by reflecting it in the origin followed by reflection in x-axis. **

**Answer**

(ii) Let Q’ be the image of Q on reflection in y-axis. Co-ordinate of Q’ will be (2, 4)

(iii) (0, k) on reflection in the origin is invariant. Co-ordinates of image will be (0, 0). k = 0

(iv) The reflection of Q in the origin is the point Q’’ and its co-ordinates will be (2, -4) and reflection of Q’’ (2, -4) in x-axis is (2, 4) which is the point Q’.

**Multiple Choice Questions**

**Choose the correct answer from the given four options (1 to 7): **

**1. The reflection of the point P (-2, 3) in the x-axis is **

**(a) (2, 3) **

**(b) (2, -3) **

**(c) (-2, -3) **

**(d) ( -2, 3)**

**Answer**

Reflection of the point P (-2, 3) in x-axis is (-2, -3) (c)

**2. The reflection of the point P (-2, 3) in the y-axis is **

**(a) (2, 3) **

**(b) (2, -3) **

**(c) (-2, -3) **

**(d) (0, 3) **

**Answer**

The reflection of the point P (-2, 3) under reflection in y-axis (2, 3) (a)

**3. If the image of the point P under reflection in the x-axis is (-3, 2), then the coordinates of the point P are **

**(a) (3, 2) **

**(b) (-3, -2)**

**(c) (3, -2) **

**(d) (-3, 0) **

**Answer**

The image of the point P under reflection in the x-axis is (-3, 2), then the co-ordinates of the point P will be (-3, -2) (b)

**4. The reflection of the point P(1, -2) in the line y = -1 is **

**(a) (-3, -2)**

**(b) (1, -4) **

**(c) (1, 4)**

**(d) (1, 0) **

**Answer**

The reflection of the point P (1, -2) in the line y = - 1 is (1, 0) (d)

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

**(a) (0, - 1)**

**(b) (8, - 1)**

**(c) (0, 1)**

**(d) none of these **

**Answer**

The reflection of A (4, -1) in the line x = 2 will be A’ (0, -1) (a)

**Question 6.** **The reflection of the point (-3, 0) in the origin is the point **

**(a) (0, -3)**

**(b) (0, 3)**

**(c) (3, 0)**

**(d) none of these **

**Answer**

Reflection of the point (-3, 0) in origin will be (3, 0) (c)

**7. Which of the following points is invariant with respect to the line y = -2 ? **

**(a) (3, 2)**

**(b) (3, -2) **

**(c) (2, 3) **

**(d) (-2, 3) **

**Answer**

The variant points are (3, -2) (b)

**Chapter Test**

**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-ordinate of P’ and P’’. Write down a single transformation that maps P onto P’’. **

**Answer**

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.

**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. **

**Answer**

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.

**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 value of a, b, c and d. **

**Answer**

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

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

**Answer**

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 images of the vertices will be A’’ (4, 1), B’’ (0, -7), C’’ (-2, -5)

**5. The point 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. **

**Answer**

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.

**6. Use a graph paper for this question (take 2cm = 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 co-ordinates. 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. **

**Answer**

(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)

**(iii)** The equation of the line of symmetry is x = 0

**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. **

**Answer**

**(i)** ∆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 at the end.

**(iii) **The figure in the diagram is a rectangle.

**(iv)** The co-ordinate 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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