Selina solutions for Mathematics [English] 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 point under reflection in x-axis:

 (3, 2)

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

(–5, 4)

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

(0, 0)

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

(6, –3)

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

(–2, –4)

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

(–6, 4)

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

(–3, 0)

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 P(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”.

1. Write down the co-ordinates of A”.
2. 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”.

1. Write down the co-ordinates of A”.
2. 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 the 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).

1. Name the line of reflection.
2. Write down the co-ordinates of the image of (5, –8) in the line obtained in (a).

Attempt this question on graph paper.

1. Plot A (3, 2) and B (5, 4) on graph paper. Take 2 cm = 1 unit on both the axes.
2. Reflect A and B in the x-axis to A’ and B’ respectively. Plot these points also on the same graph paper.
3. Write down:
   1. the geometrical name of the figure ABB’A’;
   2. the measure of angle ABB’;
   3. the image of A” of A, when A is reflected in the origin.
   4. 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.

1. Name or write equations for the lines L₁ and L₂.
2. 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.
3. Write down the images of P and Q on reflection in L₂. Name the images as P” and Q” respectively.
4. State or describe a single transformation that maps P’ onto P''.

1. Point P (a, b) is reflected in the x-axis to P’ (5, –2). Write down the values of a and b.
2. P” is the image of P when reflected in the y-axis. Write down the co-ordinates of P”.
3. 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).

1. State the name of the mirror line and write its equation.
2. 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 co-ordinates 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:

1. A’ of A under reflection in the x-axis.
2. B’ of B under reflection in the line AA’.
3. A” of A under reflection in the y-axis.
4. B” of B under reflection in the line AA”.

1. Plot the points A (3, 5) and B (–2, –4). Use 1 cm = 1 unit on both the axes.
2. 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.
3. 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.
4. Write down the geometrical name of the figure AA’BB’.
5. 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’.

1. Write down the co-ordinates of P’.
2. If M is the foot of the perpendicular from P to the x-axis, find the co-ordinates of M.
3. If N is the foot of the perpendicular from P’ to the x-axis, find the co-ordinates of N.
4. Name the figure PMP’N.
5. 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:

1. the co-ordinates of P’ and O’.
2. the length of the segments PP’ and OO’.
3. the perimeter of the quadrilateral POP’O’.
4. 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).

1. P is invariant when reflected in an axis. Name the axis.
2. Find the image of Q on reflection in the axis found in (a).
3. (0, k) on reflection in the origin is invariant. Write the value of k.
4. Write the co-ordinates of the image of Q, obtained by reflecting it in the origin followed by reflection in x-axis.

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".

1. Write down the co-ordinates of A", B" and C".
2. Write down a single transformation that maps triangle ABC onto triangle A"B"C".

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 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. State the line of symmetry of this figure.

Use a graph paper for this question.

(Take 2 cm = 1 unit on both x and y axes)

1. Plot the following points: A(0, 4), B(2, 3), C(1, 1) and D(2, 0).
2. Reflect points B, C, D on the y-axis and write down their coordinates. Name the images as B', C', D' respectively.
3. 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.