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

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

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

Question 1.
Find the co-ordinates of the images of the following points under reflection in the x- axis:
(i) (2, -5)
(ii) \(-\frac { 3 }{ 2 } ,-\frac { 1 }{ 2 } \)
(iii) (-7, 0)
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 10 Reflection Ex 10

Question 2.
Find the co-ordinates of the images of the following points under reflection in the y-axis:
(i) (2, -5)
(ii) \(-\frac { 3 }{ 2 } ,\frac { 1 }{ 2 } \)
(iii) (0, -7)
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 10 Reflection Ex 10

Question 3.
Find the co-ordinates of the images of the following points under reflection in the origin:
(i) (2, -5)
(ii) \(\frac { -3 }{ 2 } ,\frac { -1 }{ 2 } \)
(iii) (0, 0)
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 10 Reflection Ex 10

Question 4.
The image of a point P under reflection in the x-axis is (5, -2). Write down the coordinates of P.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 10 Reflection Ex 10

Question 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.
(ii) Find the co-ordinates of the image of P under reflection in the y-axis.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 10 Reflection Ex 10

Question 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.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 10 Reflection Ex 10

Question 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.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 10 Reflection Ex 10
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 10 Reflection Ex 10
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 10 Reflection Ex 10

Question 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:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 10 Reflection Ex 10
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 10 Reflection Ex 10

Question 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:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 10 Reflection Ex 10

Question 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. (2000)
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 10 Reflection Ex 10

Question 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.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 10 Reflection Ex 10
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 10 Reflection Ex 10

Question 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:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 10 Reflection Ex 10
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 10 Reflection Ex 10

Question 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. (1998)
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 10 Reflection Ex 10
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 10 Reflection Ex 10

Question 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”. (1997)
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 10 Reflection Ex 10

Question 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:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 10 Reflection Ex 10

Question 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?
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 10 Reflection Ex 10
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 10 Reflection Ex 10

Question 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:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 10 Reflection Ex 10

Question 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:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 10 Reflection Ex 10

Question 19.
The image of a point P on reflection in a line l is point P’. Describe the location of the line l.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 10 Reflection Ex 10

Question 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
(i) the x-axis
(ii) the y-axis and
(iii) the origin.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 10 Reflection Ex 10

Question 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:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 10 Reflection Ex 10

Question 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
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 10 Reflection Ex 10
(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:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 10 Reflection Ex 10

Question 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. (2007)
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 10 Reflection Ex 10

Question 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. (2001)
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 10 Reflection Ex 10
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 10 Reflection Ex 10

Question 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:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 10 Reflection Ex 10

Question 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’. (2009)
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 10 Reflection Ex 10

Question 27.
The points A (2, 3), B (4, 5) and C (7, 2) are the vertices of ∆ABC. (2006)
(i) Write down the co-ordinates of A1, B1, C1 if ∆ A1B1C1 is the image of ∆ ABC when reflected in the origin.
(ii) Write down the co-ordinates of A2, B2, C2 if ∆ A2B2C2 is the image of ∆ ABC when reflected in the x-axis.
(iii) Assign the special name to the quadrilateral BCC2B2 and find its area.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 10 Reflection Ex 10
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 10 Reflection Ex 10
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 10 Reflection Ex 10
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 10 Reflection Ex 10

Question 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:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 10 Reflection Ex 10

Question 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. (2005)
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 10 Reflection Ex 10

ML Aggarwal Class 10 Solutions for ICSE Maths