Selina solutions for Concise Mathematics Class 10 ICSE chapter 12 - Reflection [Latest edition]

Complete the following table.

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.

State the co-ordinates of the following points under reflection in x-axis:

 (3, 2)

State the co-ordinates of the following points under reflection in x-axis:

(-5, 4) 

State the co-ordinates of the following points under reflection in x-axis:

(0, 0)

State the co-ordinates of the following points under reflection in y-axis:

(i) (6, -3)

(ii) (-1, 0)

(iii) (-8, -2)

State the co-ordinates of the following points under reflection in origin:

(i) (-2, -4)

(ii) (-2, 7)

(iii) (0, 0)

State the co-ordinates of the following points under reflection in the line x = 0:

(i) (-6, 4)

(ii) (0, 5)

(iii) (3, -4)

State the co-ordinates of the following points under reflection in the line y = 0:

(i) (-3, 0)

(ii) (8, -5)

(iii) (-1, -3)

A point P is reflected in the x-axis. Co-ordinates of its image are (-4, 5). Find the co-ordinates of P.

A point P is reflected in the x-axis. Co-ordinates of its image are (-4, 5). Find the co-ordinates of the image of P under reflection in the y-axis.

A point P is reflected in the origin. Co-ordinates of its image are (-2, 7).Find the co-ordinates of P.

A point P is reflected in the origin. Co-ordinates of its image are (-2, 7). Find the co-ordinates of the image of P under reflection in the x-axis.

The point (a, b) is first reflected in the origin and then reflected in the y-axis to P’. If P’ has co-ordinates (4, 6); evaluate a and b.

The point P (x, y) is first reflected in the x-axis and reflected in the origin to P’. If P’ has co-ordinates (-8, 5); evaluate x and y.

The point A (-3, 2) is reflected in the x-axis to the point A’. Point A’ is then reflected in the origin to point A”.

(i) Write down the co-ordinates of A”.

(ii) Write down a single transformation that maps A onto A”.

The point A (4, 6) is first reflected in the origin to point A’. Point A’ is then reflected in the y-axis to the point A”.

(i) Write down the co-ordinates of A”.

(ii) Write down a single transformation that maps A onto A”.

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’B’C’. Triangle A’B’C’ is then reflected in the origin to triangle A”B”C”.

(i) Write down the co-ordinates of A”, B” and C”.

(ii) Write down a single transformation that maps triangle ABC onto triangle A”B”C”.

P and Q have co-ordinates (-2, 3) and (5, 4) respectively. Reflect P in the x-axis to P’ and Q in the y-axis to Q’. State the co-ordinates of P’ and Q’.

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).

Point A (4, -1) is reflected as A’ in the y-axis. Point B on reflection in the x-axis is mapped as B’ (-2, 5). Write down the co-ordinates of A’ and B.

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).

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’ and B’ respectively. Plot these points also on the same graph paper.

(c) Write down:

(i) the geometrical name of the figure ABB’A’;

(ii) the measure of angle ABB’;

(iii) the image of A” of A, when A is reflected in the origin.

(iv) the single transformation that maps A’ to A”.

Points (3, 0) and (-1, 0) are invariant points under reflection in the line L1;

points (0, -3) and (0, 1) are invariant points on reflection in line L2.

(i) Name or write equations for the lines L1 and L2.

(ii) Write down the images of the points P (3, 4) and Q (-5, -2) on reflection in line L1. Name the images as P’ and Q’ respectively.

(iii) Write down the images of P and Q on reflection in L2. Name the images as P” and Q” respectively. (iv) State or describe a single transformation that maps P’ onto p''

(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”.

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.

The points P (4, 1) and Q (-2, 4) are reflected in line y = 3. Find the co-ordinates of P’, the image of P and Q’, the image of Q.

A point P (-2, 3) is reflected in line x = 2 to point P’. Find the coordinates of P’.

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, 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.

Points A and B have co-ordinates (3, 4) and (0, 2) respectively. Find the image:

(a) A’ of A under reflection in the x-axis.

(b) B’ of B under reflection in the line AA’.

(c) A” of A under reflection in the y-axis.

(d) B” of B under reflection in the line AA”.

(i) Plot the points A (3, 5) and B (-2, -4). Use 1 cm = 1 unit on both the axes.

(ii) A’ is the image of A when reflected in the x-axis. Write down the co-ordinates of A’ and plot it on the graph paper.

(iii) B’ is the image of B when reflected in the y-axis, followed by reflection in the origin. Write down the co-ordinates of B’ and plot it on the graph paper.

(iv) Write down the geometrical name of the figure AA’BB’.

(v) Name the invariant points under reflection in the x-axis.

The point P (5, 3) was reflected in the origin to get the image P’.

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

(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’ to the x-axis, find the co-ordinates of N.

(d) Name the figure PMP’N.

(e) Find the area of the figure PMP’N.

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

Write:

(i) the co-ordinates of P’ and O’.

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

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

(iv) the geometrical name of the figure POP’O’.

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’, B’, C’ and D’ respectively. Locate A’, B’, C’ and D’ on the graph sheet and write their co-ordinates .

Are D, A, A’ and D’ collinear?

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.

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’, Q’ and R’, if P’Q’R’ is the image of PQR, when reflected in the origin.

(b) Write down the co-ordinates of P”, Q” and R”, if P”Q”R” is the image of PQR, when reflected in the x-axis.

(c) Mention the special name of the quadrilateral QRR”Q” and find its area.

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’ and B’.

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

(c) Sate the geometrical name for the figure ABA’B’.

(d) Find its perimeter.

Use graph paper for this question.

(Take 2 cm = 1 unit along both side x-axis and y-axis.)

Plot the points O(0,0), A(-4, 4), B(-3, 0) and C(0, -3).

1. Reflect points A and B on the y-axis and name them A' and B' respectively. Write down their co-ordinates.
2. Name the figure OABCB'A'.
3.  iii. State the line of symmetry of this figure. [Now symmetry is not in course] 

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 the y-axis and write down their coordinates. Name the images as B', C', D' respectively.

(iii) Join the points A, B, C, D, D', C', B' and A in order, so as to form a closed figure. Write down the equation to the line about which if this closed figure obtained is folded, the two parts of the figure exactly coincide.