**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)**

**Solution:**

**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)**

**Solution:**

**3. Find the 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)**

**Solution:**

**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.**

**Solution:**

**9. The point P ( -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”.**

**Solution:**

**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 a reflection in the y-axis**

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

**Solution:**

**12. If P’ (-4,-3) is the image of a point P under reflection 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.**

**Solution:**

**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.**

**Solution:**

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

**Solution:**

**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’.**

**Solution:**

**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?**

**Solution:**

**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.**

**Solution:**

**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”.**

**Solution:**

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

**Solution:**

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

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

**(iii) the origin.**

**Solution:**

**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.**

**Solution:**

**22. A (-2,4) and B (-4,2) are reflected in the y-axis. If A’ and B’ are images of A and B respectively, find**

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

**(ii) Assign a special name to a quad. AA’B’B.**

**(iii) State whether AB’ = BA’.**

**Solution:**

**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.**

**Solution:**

**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 the 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.**

**Solution:**

**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.**

**Solution:**

**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 the 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’.**

**Solution:**

**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’.**

**Solution:**

**29. Use a graph paper 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 a reflection in x-axis.**

**Solution:**

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

**Solution:**

**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**

**Solution:**

**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.**

**Solution:**

**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.**

**Solution:**

**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.**

**Solution:**

**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 y-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.**

**Solution:**

**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.**

**Solution:**