Class X ICSE Maths Chapter Reflection Exercise 10
Welcome to our dedicated collection of questions on the topic of "Reflection," designed to help you understand and apply this fundamental concept in geometry. Our question bank covers key topics such as reflecting points, lines, and shapes across axes and planes, as well as understanding the properties of reflected images. These questions are perfect for students looking to strengthen their grasp of geometric transformations and improve their problem-solving skills. Whether you're preparing for exams or aiming to deepen your knowledge, our carefully curated collection offers the ideal resource to master the concept of "Reflection."
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Q1 Find the coordinates of the images of the following points under reflection in the X-axis :
(i) (2, -5)
(ii) (-3/2 , -1/2)
(iii) (-7, 0).
Q2 Find the coordinates of the images of the following points under reflection in the y-axis:
(i) (2, -5)
(ii) (-3/2 , 1/2)
(iii) (0, -7).
Q3 Find the coordinates of the images of the following points under reflection in the origin:
(i) (2, -5)
(ii) (-3/2, -1/2)
(iii) (0, 0)
.
Q4 The image of a point P under reflection in the x-axis is (5,-2). Write down the coordinates of P.
Q5 A point P is reflected in the x-axis. Coordinates of its image are (8, —6).
(i) Find the coordinates of P.
(ii) Find the coordinates of the image of P under reflection in the y-axis.
Q6 A point P is reflected in the origin. Coordinates of its image are (2, —5). Find
(i) the coordinates of P.
(ii) the coordinates of the image of P in the x-axis.
Q7 (i) The point P(2, 3) is reflected in the line x = 4 to the point P’. Find the coordinates of the point P’.
(ii) Find the image of the point P(1, —2) in the line x = -1.
Q8 (i) The point P(2, 4) on reflection in the line y = 1 is mapped onto P’. Find the coordinates of P’.
(ii) Find the image of the point P(-3, —5) in the line y = -2.
Q9 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 coordinates of P’ and P”. Write down a single transformation that maps P onto P”.
Q10 Write down the coordinates 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.
Q11 Find the coordinates of the image of (3, 1) under reflection in x-axis followed by reflection in the line x = 1.
Q12 If P’(—4, —3) is the image of a point P under reflection in the origin, find
(i) the coordinates of P.
(ii) the coordinates of the image of P under reflection in the line y = -2.
Q13 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 coordinates of P”. Find the coordinates of P” when P is reflected in the line, parallel to y-axis such that x = 4.
Q14 (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 coordinates of P”.
(iii) Name a single transformation that maps P’ to P”.
Q15 Points A and B have coordinates (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’
Q16 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?
Q17 The points (6, 2), (3, -1) and (-2, 4) are the vertices of a right angled triangle. Check whether it remains a night angled triangle after reflection in the y-axis
Q18 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 coordinates of A”B”C”. Write down a single transformation that maps ABC onto A”B”C”.
Q19 The image of 2 point P on reflection in a line l is point P’. Describe the location of the line l
Q20 Given two posts P and Q, and that (1) the image of P on reflection in y-axis is the point O 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.
Q21 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 coordinates of the image of (-3, -4) in the mirror line.
Q22 Use graph paper for this question (take 2 cm = 1 unit along 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.
Q23 Use 2 graph sheet for this question. Take 1 cm = 1 unit along both x and y-axes.
(i) Plot the points: A (0, 5), B(3, 0), C(1, 0) and D(1, —5). (ii) Reflect the points B, C and D on the y-axis and name them as B’, C’ and D’ respectively.
(iii) Write down the coordinates of B', C’ and D’.
(iv) Join the points A, B,C, D, D', C’, B’, A in order and give a name to the closed figure ABCDD'C'B’.
Q24 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 coordinates of Q.
(ii) Point Q is reflected about the line y = 0 to get the image R. Find the coordinates of K
(iii) Name the figure POR.
(iv) Find the area of the figure POR.
Q25 Using 2 graph paper, plot the points A(6, 4) and B(0, 4).
(i) Reflect A and B in the origin to get images A’ and B’.
(ii) Write the coordinates of A’ and B’. (iii) Sate the geometrical name for the figure ABA’B’.
(iv) Find its perimeter
Q26 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 the x-axis, write the coordinates of A’.
(iii) If B’ is the image of B when reflected in the line AA’, write the coordinates of B’.
(iv) Give the geometrical name for the figure ABA’B’.
Q27 The points A(2, 3), B(4, 5) and C(7, 2) are the vertices of △ABC.
(i) Write down the coordinates of A1, B1, C1 if △A1B1C1 is the image of △ABC when reflected in the origin.
(i) Write down the coordinates 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.
Q28 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 coordinates of P’ and O’.
(ii) the length of segments PP’ and OO’.
(iii) the perimeter of the quadrilateral POP’O’.
Q29 Use a graph paper for this question. (Take 10 small divisions = 1 unit on both axes).
P and Q have coordinates (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 coordinates of the image of Q, obtained by reflecting it in the origin followed by reflection in x-axis.
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