{"id":591863,"date":"2022-04-25T05:11:10","date_gmt":"2022-04-25T05:11:10","guid":{"rendered":"https:\/\/www.indcareer.com\/schools\/?p=591863"},"modified":"2022-04-25T09:43:30","modified_gmt":"2022-04-25T09:43:30","slug":"selina-class-10-icse-solutions-mathematics-chapter-12-reflection","status":"publish","type":"post","link":"https:\/\/www.indcareer.com\/schools\/selina-class-10-icse-solutions-mathematics-chapter-12-reflection\/","title":{"rendered":"Selina Class 10 ICSE Solutions Mathematics : Chapter 12-\u00a0Reflection"},"content":{"rendered":"\n

Class 10: Maths Chapter 12 solutions. Complete Class 10 Maths Chapter 12 Notes.<\/p>\n\n\n\n

Selina Class 10 ICSE Solutions Mathematics : Chapter 12- Reflection<\/h2>\n\n\n\n

Selina 10th Maths Chapter 12, Class 10 Maths Chapter 12 solutions<\/p>\n\n\n\n

Exercise 12A<\/h3>\n\n\n\n

Question 1.<\/strong>
Complete the following table:<\/p>\n\n\n\n

Point<\/td>Transformation<\/td>Image<\/td><\/tr>
(5, -7)<\/td><\/td>(-5, 7)<\/td><\/tr>
(4, 2)<\/td>Reflection in x-axis<\/td><\/td><\/tr>
<\/td>Reflection in y-axis<\/td>(0, 6)<\/td><\/tr>
(6, -6)<\/td><\/td>(-6, 6)<\/td><\/tr>
(4, -8)<\/td><\/td>(-4, -8)<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

Solution:<\/strong><\/p>\n\n\n\n

Point<\/strong><\/td>Transformation<\/strong><\/td>Image<\/strong><\/td><\/tr>
(5, -7)<\/td>Reflection in origin<\/td>(-5, 7)<\/td><\/tr>
(4, 2)<\/td>Reflection in x-axis<\/td>(4, -2)<\/td><\/tr>
(0, 6)<\/td>Reflection in y-axis<\/td>(0, 6)<\/td><\/tr>
(6, -6)<\/td>Reflection in origin<\/td>(-6, 6)<\/td><\/tr>
(4, -8)<\/td>Reflection in y-axis<\/td>(-4, -8)<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

Question 2.<\/strong>
A point P is its own image under the reflection in a line l. Describe the position of point the P with respect to the line l.
Solution:<\/strong>
Since, the point P is its own image under the reflection in the line l. So, point P is an invariant point.
Hence, the position of point P remains unaltered.<\/p>\n\n\n\n

Question 3.<\/strong>
State the co-ordinates of the following points under reflection in x-axis:
(i) (3, 2)
(ii) (-5, 4)
(iii) (0, 0)
Solution:<\/strong>
(i) (3, 2)
The co-ordinate of the given point under reflection in the x-axis is (3, -2).
(ii) (-5, 4)
The co-ordinate of the given point under reflection in the x-axis is (-5, -4).
(iii) (0, 0)
The co-ordinate of the given point under reflection in the x-axis is (0, 0).<\/p>\n\n\n\n

Question 4.<\/strong>
State the co-ordinates of the following points under reflection in y-axis:
(i) (6, -3)
(ii) (-1, 0)
(iii) (-8, -2)
Solution:<\/strong>
(i) (6, -3)
The co-ordinate of the given point under reflection in the y-axis is (-6, -3).
(ii) (-1, 0)
The co-ordinate of the given point under reflection in the y-axis is (1, 0).
(iii) (-8, -2)
The co-ordinate of the given point under reflection in the y-axis is (8, -2).<\/p>\n\n\n\n

Question 5.<\/strong>
State the co-ordinates of the following points under reflection in origin:
(i) (-2, -4)
(ii) (-2, 7)
(iii) (0, 0)
Solution:<\/strong>
(i) (-2, -4)
The co-ordinate of the given point under reflection in origin is (2, 4).
(ii) (-2, 7)
The co-ordinate of the given point under reflection in origin is (2, -7).
(iii) (0, 0)
The co-ordinate of the given point under reflection in origin is (0, 0).<\/p>\n\n\n\n

Question 6.<\/strong>
State the co-ordinates of the following points under reflection in the line x = 0:
(i) (-6, 4)
(ii) (0, 5)
(iii) (3, -4)
Solution:<\/strong>
(i) (-6, 4)
The co-ordinate of the given point under reflection in the line x = 0 is (6, 4).
(ii) (0, 5)
The co-ordinate of the given point under reflection in the line x = 0 is (0, 5).
(iii) (3, -4)
The co-ordinate of the given point under reflection in the line x = 0 is (-3, -4).<\/p>\n\n\n\n

Question 7.<\/strong>
State the co-ordinates of the following points under reflection in the line y = 0:
(i) (-3, 0)
(ii) (8, -5)
(iii) (-1, -3)
Solution:<\/strong>
(i) (-3, 0)
The co-ordinate of the given point under reflection in the line y = 0 is (-3, 0).
(ii) (8, -5)
The co-ordinate of the given point under reflection in the line y = 0 is (8, 5).
(iii) (-1, -3)
The co-ordinate of the given point under reflection in the line y = 0 is (-1, 3).<\/p>\n\n\n\n

Question 8.<\/strong>
A point P is reflected in the x-axis. Co-ordinates of its image are (-4, 5).
(i) Find the co-ordinates of P.
(ii) Find the co-ordinates of the image of P under reflection in the y-axis.
Solution:<\/strong>
(i) Since, Mx<\/sub> (-4, -5) = (-4, 5)
So, the co-ordinates of P are (-4, -5).
(ii) Co-ordinates of the image of P under reflection in the y-axis (4, -5).<\/p>\n\n\n\n

Question 9.<\/strong>
A point P is reflected in the origin. Co-ordinates of its image are (-2, 7).
(i) Find the co-ordinates of P.
(ii) Find the co-ordinates of the image of P under reflection in the x-axis.
Solution:<\/strong>
(i) Since, MO<\/sub> (2, -7) = (-2, 7)
So, the co-ordinates of P are (2, -7).
(ii) Co-ordinates of the image of P under reflection in the x-axis (2, 7).<\/p>\n\n\n\n

Question 10.<\/strong>
The point (a, b) is first reflected in the origin and then reflected in the y-axis to P\u2019. If P\u2019 has co-ordinates (4, 6); evaluate a and b.
Solution:<\/strong>
MO<\/sub> (a, b) = (-a, -b)
My<\/sub> (-a, -b) = (a, -b)
Thus, we get the co-ordinates of the point P\u2019 as (a, -b). It is given that the co-ordinates of P\u2019 are (4, 6).
On comparing the two points, we get, a = 4 and b = -6<\/p>\n\n\n\n

Question 11.<\/strong>
The point P (x, y) is first reflected in the x-axis and reflected in the origin to P\u2019. If P\u2019 has co-ordinates (-8, 5); evaluate x and y.
Solution:<\/strong>
Mx<\/sub> (x, y) = (x, -y)
MO<\/sub> (x, -y) = (-x, y)
Thus, we get the co-ordinates of the point P\u2019 as (-x, y). It is given that the co-ordinates of P\u2019 are (-8, 5).
On comparing the two points, we get, x = 8 and y = 5<\/p>\n\n\n\n

Question 12.<\/strong>
The point A (-3, 2) is reflected in the x-axis to the point A\u2019. Point A\u2019 is then reflected in the origin to point A\u201d.
(i) Write down the co-ordinates of A\u201d.
(ii) Write down a single transformation that maps A onto A\u201d.
Solution:<\/strong>
(i) The reflection in x-axis is given by Mx<\/sub> (x, y) = (x, -y).
A\u2019 = reflection of A (-3, 2) in the x- axis = (-3, -2).
The reflection in origin is given by MO<\/sub> (x, y) = (-x, -y).
A\u201d = reflection of A\u2019 (-3, -2) in the origin = (3, 2)
(ii) The reflection in y-axis is given by My<\/sub> (x, y) = (-x, y).
The reflection of A (-3, 2) in y-axis is (3, 2).
Thus, the required single transformation is the reflection of A in the y-axis to the point A\u201d.<\/p>\n\n\n\n

Question 13.<\/strong>
The point A (4, 6) is first reflected in the origin to point A\u2019. Point A\u2019 is then reflected in the y-axis to the point A\u201d.
(i) Write down the co-ordinates of A\u201d.
(ii) Write down a single transformation that maps A onto A\u201d.
Solution:<\/strong>
(i) The reflection in origin is given by MO<\/sub> (x, y) = (-x, -y).
A\u2019 = reflection of A (4, 6) in the origin = (-4, -6)
The reflection in y-axis is given by My<\/sub> (x, y) = (-x, y).
A\u201d = reflection of A\u2019 (-4, -6) in the y-axis = (4, -6)
(ii) The reflection in x-axis is given by Mx<\/sub> (x, y) = (x, -y).
The reflection of A (4, 6) in x-axis is (4, -6).
Thus, the required single transformation is the reflection of A in the x-axis to the point A\u201d.<\/p>\n\n\n\n

Question 14.<\/strong>
The triangle ABC, where A is (2, 6), B is (-3, 5) and C is (4, 7), is reflected in the y-axis to triangle A\u2019B\u2019C\u2019. Triangle A\u2019B\u2019C\u2019 is then reflected in the origin to triangle A\u201dB\u201dC\u201d.
(i) Write down the co-ordinates of A\u201d, B\u201d and C\u201d.
(ii) Write down a single transformation that maps triangle ABC onto triangle A\u201dB\u201dC\u201d.
Solution:<\/strong>
(i) Reflection in y-axis is given by My<\/sub> (x, y) = (-x, y)
\u2234 A\u2019 = Reflection of A (2, 6) in y-axis = (-2, 6)
Similarly, B\u2019 = (3, 5) and C\u2019 = (-4, 7)
Reflection in origin is given by MO<\/sub> (x, y) = (-x, -y)
\u2234 A\u201d = Reflection of A\u2019 (-2, 6) in origin = (2, -6)
Similarly, B\u201d = (-3, -5) and C\u201d = (4, -7)
(ii) A single transformation which maps triangle ABC to triangle A\u201dB\u201dC\u201d is reflection in x-axis.<\/p>\n\n\n\n

Question 15.<\/strong>
P and Q have co-ordinates (-2, 3) and (5, 4) respectively. Reflect P in the x-axis to P\u2019 and Q in the y-axis to Q\u2019. State the co-ordinates of P\u2019 and Q\u2019.
Solution:<\/strong>
Reflection in x-axis is given by Mx<\/sub> (x, y) = (x, -y)
P\u2019 = Reflection of P(-2, 3) in x-axis = (-2, -3)
Reflection in y-axis is given by My<\/sub> (x, y) = (-x, y)
Q\u2019 = Reflection of Q(5, 4) in y-axis = (-5, 4)
Thus, the co-ordinates of points P\u2019 and Q\u2019 are (-2, -3) and (-5, 4) respectively.<\/p>\n\n\n\n

Question 16.<\/strong>
On a graph paper, plot the triangle ABC, whose vertices are at points A (3, 1), B (5, 0) and C (7, 4).
On the same diagram, draw the image of the triangle ABC under reflection in the origin O (0, 0).
Solution:<\/strong>
The graph shows triangle ABC and triangle A\u2019B\u2019C\u2019 which is obtained when ABC is reflected in the origin.
\"Selina<\/p>\n\n\n\n

Question 17.<\/strong>
Find the image of point (4, -6) under the following operations:
(i) Mx<\/sub> . My<\/sub> (ii) My<\/sub> . Mx<\/sub>
(iii) MO<\/sub> . Mx<\/sub> (iv) Mx<\/sub> . MO<\/sub>
(v) MO<\/sub> . My<\/sub> (vi) My<\/sub> . MO<\/sub>
Write down a single transformation equivalent to each operation given above. State whether:
(a) MO<\/sub> . Mx<\/sub> = Mx<\/sub> . MO<\/sub>
(b) My<\/sub> . MO<\/sub> = MO<\/sub> . My<\/sub>
Solution:<\/strong>
(i) Mx<\/sub> . My <\/sub>(4, -6) = Mx<\/sub> (-4, -6) = (-4, 6)
Single transformation equivalent to Mx<\/sub> . My<\/sub> is MO<\/sub>.
(ii) My<\/sub> . Mx <\/sub>(4, -6) = My<\/sub> (4, 6) = (-4, 6)
Single transformation equivalent to My<\/sub> . Mx<\/sub> is MO<\/sub>.
(iii) MO<\/sub> . Mx <\/sub>(4, -6) = MO<\/sub> (4, 6) = (-4, -6)
Single transformation equivalent to MO<\/sub> . Mx<\/sub> is My<\/sub>.
(iv) Mx<\/sub> . MO <\/sub>(4, -6) = Mx<\/sub> (-4, 6) = (-4, -6)
Single transformation equivalent to Mx<\/sub> . MO<\/sub> is My<\/sub>.
(v) MO<\/sub> . My <\/sub>(4, -6) = MO<\/sub> (-4, -6) = (4, 6)
Single transformation equivalent to MO<\/sub> . My<\/sub> is Mx<\/sub>.
(vi) My<\/sub> . MO <\/sub>(4, -6) = My<\/sub> (-4, 6) = (4, 6)
Single transformation equivalent to Mx<\/sub> . MO<\/sub> is Mx<\/sub>.
From (iii) and (iv), it is clear that MO<\/sub> . Mx<\/sub> = Mx<\/sub> . MO<\/sub>.
From (v) and (vi), it is clear that My<\/sub> . MO<\/sub> = MO<\/sub> . My<\/sub>.<\/p>\n\n\n\n

Question 18.<\/strong>
Point A (4, -1) is reflected as A\u2019 in the y-axis. Point B on reflection in the x-axis is mapped as B\u2019 (-2, 5). Write down the co-ordinates of A\u2019 and B.
Solution:<\/strong>
Reflection in y-axis is given by My<\/sub> (x, y) = (-x, y)
A\u2019 = Reflection of A(4, -1) in y-axis = (-4, -1)
Reflection in x-axis is given by Mx<\/sub> (x, y) = (x, -y)
B\u2019 = Reflection of B in x-axis = (-2, 5)
Thus, B = (-2, -5)<\/p>\n\n\n\n

Question 19.<\/strong>
The point (-5, 0) on reflection in a line is mapped as (5, 0) and the point (-2, -6) on reflection in the same line is mapped as (2, -6).
(a) Name the line of reflection.
(b) Write down the co-ordinates of the image of (5, -8) in the line obtained in (a).
Solution:<\/strong>
(a) We know that reflection in the line x = 0 is the reflection in the y-axis.
It is given that:
Point (-5, 0) on reflection in a line is mapped as (5, 0).
Point (-2, -6) on reflection in the same line is mapped as (2, -6).
Hence, the line of reflection is x = 0.
(b) It is known that My<\/sub> (x, y) = (-x, y)
Co-ordinates of the image of (5, -8) in the line x = 0 are (-5, -8).<\/p>\n\n\n\n

Exercise 12B<\/h3>\n\n\n\n

Question 1.<\/strong>
Attempt this question on graph paper.
(a) Plot A (3, 2) and B (5, 4) on graph paper. Take 2 cm = 1 unit on both the axes.
(b) Reflect A and B in the x-axis to A\u2019 and B\u2019 respectively. Plot these points also on the same graph paper.
(c) Write down:
(i) the geometrical name of the figure ABB\u2019A\u2019;
(ii) the measure of angle ABB\u2019;
(iii) the image of A\u201d of A, when A is reflected in the origin.
(iv) the single transformation that maps A\u2019 to A\u201d.
Solution:<\/strong>
\"Selina
(c)
(i) From graph, it is clear that ABB\u2019A\u2019 is an isosceles trapezium.
(ii) The measure of angle ABB\u2019 is 45\u00b0.
(iii) A\u201d = (-3, -2)
(iv) Single transformation that maps A\u2019 to A\u201d is the reflection in y-axis.<\/p>\n\n\n\n

Question 2.<\/strong>
Points (3, 0) and (-1, 0) are invariant points under reflection in the line L1<\/sub>; points (0, -3) and (0, 1) are invariant points on reflection in line L2<\/sub>.
(i) Name or write equations for the lines L1<\/sub> and L2<\/sub>.
(ii) Write down the images of the points P (3, 4) and Q (-5, -2) on reflection in line L1<\/sub>. Name the images as P\u2019 and Q\u2019 respectively.
(iii) Write down the images of P and Q on reflection in L2<\/sub>. Name the images as P\u201d and Q\u201d respectively.
(iv) State or describe a single transformation that maps P\u2019 onto P\u201d.
Solution:<\/strong>
(i) We know that every point in a line is invariant under the reflection in the same line.
Since points (3, 0) and (-1, 0) lie on the x-axis.
So, (3, 0) and (-1, 0) are invariant under reflection in x-axis.
Hence, the equation of line L1<\/sub> is y = 0.
Similarly, (0, -3) and (0, 1) are invariant under reflection in y-axis.
Hence, the equation of line L2<\/sub> is x = 0.
(ii) P\u2019 = Image of P (3, 4) in L1<\/sub> = (3, -4)
Q\u2019 = Image of Q (-5, -2) in L1<\/sub> = (-5, 2)
(iii) P\u201d = Image of P (3, 4) in L2<\/sub> = (-3, 4)
Q\u201d = Image of Q (-5, -2) in L2<\/sub> = (5, -2)
(iv) Single transformation that maps P\u2019 onto P\u201d is reflection in origin.<\/p>\n\n\n\n

Question 3.<\/strong>
(i) Point P (a, b) is reflected in the x-axis to P\u2019 (5, -2). Write down the values of a and b.
(ii) P\u201d is the image of P when reflected in the y-axis. Write down the co-ordinates of P\u201d.
(iii) Name a single transformation that maps P\u2019 to P\u201d.
Solution:<\/strong>
(i) We know Mx<\/sub> (x, y) = (x, -y)
P\u2019 (5, -2) = reflection of P (a, b) in x-axis.
Thus, the co-ordinates of P are (5, 2).
Hence, a = 5 and b = 2.
(ii) P\u201d = image of P (5, 2) reflected in y-axis = (-5, 2)
(iii) Single transformation that maps P\u2019 to P\u201d is the reflection in origin.<\/p>\n\n\n\n

Question 4.<\/strong>
The point (-2, 0) on reflection in a line is mapped to (2, 0) and the point (5, -6) on reflection in the same line is mapped to (-5, -6).
(i) State the name of the mirror line and write its equation.
(ii) State the co-ordinates of the image of (-8, -5) in the mirror line.
Solution:<\/strong>
(i) We know reflection of a point (x, y) in y-axis is (-x, y).
Hence, the point (-2, 0) when reflected in y-axis is mapped to (2, 0).
Thus, the mirror line is the y-axis and its equation is x = 0.
(ii) Co-ordinates of the image of (-8, -5) in the mirror line (i.e., y-axis) are (8, -5).<\/p>\n\n\n\n

Question 5.<\/strong>
The points P (4, 1) and Q (-2, 4) are reflected in line y = 3. Find the co-ordinates of P\u2019, the image of P and Q\u2019, the image of Q.
Solution:<\/strong>
The line y = 3 is a line parallel to x-axis and at a distance of 3 units from it.
Mark points P (4, 1) and Q (-2, 4).
From P, draw a straight line perpendicular to line CD and produce. On this line mark a point P\u2019 which is at the same distance above CD as P is below it.
The co-ordinates of P\u2019 are (4, 5).
Similarly, from Q, draw a line perpendicular to CD and mark point Q\u2019 which is at the same distance below CD as Q is above it.
The co-ordinates of Q\u2019 are (-2, 2).
\"Selina<\/p>\n\n\n\n

Question 6.<\/strong>
A point P (-2, 3) is reflected in line x = 2 to point P\u2019. Find the coordinates of P\u2019.
Solution:<\/strong>
The line x = 2 is a line parallel to y-axis and at a distance of 2 units from it.
Mark point P (-2, 3).
From P, draw a straight line perpendicular to line CD and produce. On this line mark a point P\u2019 which is at the same distance to the right of CD as P is to the left of it.
The co-ordinates of P\u2019 are (6, 3).
\"Selina<\/p>\n\n\n\n

Question 7.<\/strong>
A point P (a, b) is reflected in the x-axis to P\u2019 (2, -3). Write down the values of a and b. P\u201d is the image of P, reflected in the y-axis. Write down the co-ordinates of P\u201d. Find the co-ordinates of P\u201d\u2019, when P is reflected in the line, parallel to y-axis, such that x = 4.
Solution:<\/strong>
\"Selina
A point P (a, b) is reflected in the x-axis to P\u2019 (2, -3).
We know Mx<\/sub> (x, y) = (x, -y)
Thus, co-ordinates of P are (2, 3). Hence, a = 2 and b = 3.
P\u201d = Image of P reflected in the y-axis = (-2, 3)
P\u201d\u2019 = Reflection of P in the line (x = 4) = (6, 3)<\/p>\n\n\n\n

Question 8.<\/strong>
Points A and B have co-ordinates (3, 4) and (0, 2) respectively. Find the image:
(a) A\u2019 of A under reflection in the x-axis.
(b) B\u2019 of B under reflection in the line AA\u2019.
(c) A\u201d of A under reflection in the y-axis.
(d) B\u201d of B under reflection in the line AA\u201d.
Solution:<\/strong>
\"Selina
(a) A\u2019 = Image of A under reflection in the x-axis = (3, -4)
(b) B\u2019 = Image of B under reflection in the line AA\u2019 = (6, 2)
(c) A\u201d = Image of A under reflection in the y-axis = (-3, 4)
(d) B\u201d = Image of B under reflection in the line AA\u201d = (0, 6)<\/p>\n\n\n\n

Question 9.<\/strong>
(i) Plot the points A (3, 5) and B (-2, -4). Use 1 cm = 1 unit on both the axes.
(ii) A\u2019 is the image of A when reflected in the x-axis. Write down the co-ordinates of A\u2019 and plot it on the graph paper.
(iii) B\u2019 is the image of B when reflected in the y-axis, followed by reflection in the origin. Write down the co-ordinates of B\u2019 and plot it on the graph paper.
(iv) Write down the geometrical name of the figure AA\u2019BB\u2019.
(v) Name the invariant points under reflection in the x-axis.
Solution:<\/strong>
\"Selina
(i) The points A (3, 5) and B (-2, -4) can be plotted on a graph as shown.
(ii) A\u2019 = Image of A when reflected in the x-axis = (3, -5)
(iii) C = Image of B when reflected in the y-axis = (2, -4)
B\u2019 = Image when C is reflected in the origin = (-2, 4)
(iv) Isosceles trapezium
(v) Any point that remains unaltered under a given transformation is called an invariant.
Thus, the required two points are (3, 0) and (-2, 0).<\/p>\n\n\n\n

Question 10.<\/strong>
The point P (5, 3) was reflected in the origin to get the image P\u2019.
(a) Write down the co-ordinates of P\u2019.
(b) If M is the foot if the perpendicular from P to the x-axis, find the co-ordinates of M.
(c) If N is the foot if the perpendicular from P\u2019 to the x-axis, find the co-ordinates of N.
(d) Name the figure PMP\u2019N.
(e) Find the area of the figure PMP\u2019N.
Solution:<\/strong>
\"Selina
(a) Co-ordinates of P\u2019 = (-5, -3)
(b) Co-ordinates of M = (5, 0)
(c) Co-ordinates of N = (-5, 0)
(d) PMP\u2019N is a parallelogram.
(e) Are of PMP\u2019N = 2 (Area of D PMN)
= 2 \u00d7 \u00bd \u00d7 10 \u00d7 3
= 30 sq. units<\/p>\n\n\n\n

Question 11.<\/strong>
The point P (3, 4) is reflected to P\u2019 in the x-axis; and O\u2019 is the image of O (the origin) when reflected in the line PP\u2019. Write:
(i) the co-ordinates of P\u2019 and O\u2019.
(ii) the length of the segments PP\u2019 and OO\u2019.
(iii) the perimeter of the quadrilateral POP\u2019O\u2019.
(iv) the geometrical name of the figure POP\u2019O\u2019.
Solution:<\/strong>
\"Selina
(i) Co-ordinates of P\u2019 and O\u2019 are (3, -4) and (6, 0) respectively.
(ii) PP\u2019 = 8 units and OO\u2019 = 6 units.
(iii) From the graph it is clear that all sides of the quadrilateral POP\u2019O\u2019 are equal.
In right \u0394 PO\u2019Q,
PO\u2019 = \u221a(4)2<\/sup> + (3)2<\/sup> = 5 units
So, perimeter of quadrilateral POP\u2019O\u2019 = 4 PO\u2019 = 4 \u00d7 5 units = 20 units
(iv) Quadrilateral POP\u2019O\u2019 is a rhombus.<\/p>\n\n\n\n

Question 12.<\/strong>
A (1, 1), B (5, 1), C (4, 2) and D (2, 2) are vertices of a quadrilateral. Name the quadrilateral ABCD. A, B, C, and D are reflected in the origin on to A\u2019, B\u2019, C\u2019 and D\u2019 respectively. Locate A\u2019, B\u2019, C\u2019 and D\u2019 on the graph sheet and write their co-ordinates. Are D, A, A\u2019 and D\u2019 collinear?
Solution:<\/strong>
\"Selina
Quadrilateral ABCD is an isosceles trapezium.
Co-ordinates of A\u2019, B\u2019, C\u2019 and D\u2019 are A'(-1, -1), B'(-5, -1), C'(-4, -2) and D'(-2, -2) respectively.
It is clear from the graph that D, A, A\u2019 and D\u2019 are collinear.<\/p>\n\n\n\n

Question 13.<\/strong>
P and Q have co-ordinates (0, 5) and (-2, 4).
(a) P is invariant when reflected in an axis. Name the axis.
(b) Find the image of Q on reflection in the axis found in (i).
(c) (0, k) on reflection in the origin is invariant. Write the value of k.
(d) Write the co-ordinates of the image of Q, obtained by reflecting it in the origin followed by reflection in x-axis.
Solution:<\/strong>
(a) Any point that remains unaltered under a given transformation is called an invariant.
It is given that P (0, 5) is invariant when reflected in an axis. Clearly, when P is reflected in the y-axis then it will remain invariant. Thus, the required axis is the y-axis.
(b) The co-ordinates of the image of Q (-2, 4) when reflected in y-axis is (2, 4).
(c) (0, k) on reflection in the origin is invariant. We know the reflection of origin in origin is invariant. Thus, k = 0.
(d) Co-ordinates of image of Q (-2, 4) when reflected in origin = (2, -4)
Co-ordinates of image of (2, -4) when reflected in x-axis = (2, 4)
Thus, the co-ordinates of the point are (2, 4).<\/p>\n\n\n\n

Question PQ.<\/strong>
The points P (1, 2), Q (3, 4) and R (6, 1) are the vertices of PQR.
(a) Write down the co-ordinates of P\u2019, Q\u2019 and R\u2019, if P\u2019Q\u2019R\u2019 is the image of PQR, when reflected in the origin.
(b) Write down the co-ordinates of P\u201d, Q\u201d and R\u201d, if P\u201dQ\u201dR\u201d is the image of PQR, when reflected in the x-axis.
(c) Mention the special name of the quadrilateral QRR\u201dQ\u201d and find its area.
Solution:<\/strong>
\"Selina
(a) The co-ordinates of P\u2019, Q\u2019 and R\u2019 are (-1, -2), (-3, -4) and (-6, -1) respectively.
(b) The co-ordinates of P\u201d, Q\u201d and R\u201d are (1, -2), (3, -4) and (6, -1) respectively.
(c) The quadrilateral QRR\u201dQ\u201d is an isosceles trapezium.
Area of QRR\u201dQ\u201d = \u00bd (RR\u201d+ QQ\u201d) \u00d7 Height
= \u00bd (2 + 8) \u00d7 3 = 15 sq units<\/p>\n\n\n\n

Question 14.<\/strong>
(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) The point Q is reflected about the line y = 0 to get the image R. Find the co-ordinates or R.
(iii) Name the figure PQR.
(iv) Find the area of figure PQR.
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question PQ.<\/strong>
A\u2019 and B\u2019 are images of A (-3, 5) and B (-5, 3) respectively on reflection in y-axis. Find:
(a) the co-ordinates of A\u2019 and B\u2019.
(b) Assign special name of quadrilateral AA\u2019B\u2019B.
(c) Are AB\u2019 and BA\u2019 equal in length?
Solution:<\/strong>
\"Selina
(a) The co-ordinates of A\u2019 and B\u2019 are (3, 5) and (5, 3).
(b) Quadrilateral AA\u2019B\u2019B is an isosceles trapezium.
(c) Yes, AB\u2019 and BA\u2019 are equal in length.<\/p>\n\n\n\n

Question 15.<\/strong>
Using a graph paper, plot the point A (6, 4) and B (0, 4).
(a) Reflect A and B in the origin to get the image A\u2019 and B\u2019.
(b) Write the co-ordinates of A\u2019 and B\u2019.
(c) Sate the geometrical name for the figure ABA\u2019B\u2019.
(d) Find its perimeter.
Solution:<\/strong>
\"Selina<\/p>\n\n\n\n

Question 16.
<\/strong>Use graph paper for this question. (Take 2 cm = 1 unit along both x and y axis. Plot the points O (0, 0), A (-4, 4), B (-3, 0) and C (0, -3)
(i) Reflect points A and B on the y-axis and name them A\u2019 and B\u2019 respectively. Write down their coordinates.
(ii) Name the figure OABCB\u2019A\u2019.
(iii) State the line of symmetry of this figure.
Solution:
<\/strong>\"Selina-Concise-Mathematics-Class-10-ICSE-Solutions-Reflection<\/p>\n\n\n\n

  1. A\u2019 = (4, 4) AND B\u2019 = (3, 0)<\/li>
  2. The figure is an arrow head.<\/li>
  3. The y-axis i.e. x = 0 is the line of symmetry of figure OABCB\u2019A\u2019.<\/li><\/ol>\n\n\n\n

    Question 17.<\/strong><\/p>\n\n\n\n

    \"Selina-Concise-Mathematics-Class-10-ICSE-Solutions-Reflection<\/figure>\n\n\n\n

    (i) Plotting A(0, 4), B(2, 3), C(1, 1) and D(2, 0).
    (ii) Reflected points B'(-2, 3), C'(-1, 1) and D'(-2, 0).
    (iii) The figure is symmetrical about x = 0<\/p>\n\n\n\n

    Download PDF<\/strong><\/h2>\n\n\n\n

    Selina Class 10 ICSE Solutions Mathematics : Chapter 12- Reflection<\/p>\n\n\n\n

    Download PDF<\/strong>: Selina Class 10 ICSE Solutions Mathematics : Chapter 12-\u00a0Reflection PDF<\/a><\/p>\n\n\n\n

    Chapterwise Selina Publishers ICSE Solutions for Class 10 Maths :<\/strong><\/h2>\n\n\n\n