Class 8 Maths Solution | Lesson 19 Transformation | CDC

Reflection

Exercise 19.1

1. Write the coordinates of the image of the following co-ordinates after reflection in X-axis using graph paper.

Solution:

When a point (x, y) is reflected in the X-axis, the new coordinates become (x, -y).

(a) A(1,2) → A'(1,-2)

(b) M(2,3) → M'(2,-3)

(c) C(4,5) → C'(4,-5)

(d) D(6,6) → D'(6,-6)

(e) E(5,4) → E'(5,-4)

(f) F(2,5) → F'(2,-5)

(g) G(9,8) → G'(9,-8)

(h) H(3,9) → H'(3,-9)

2. Write the points of QN 1 in graph paper after reflecting in Y-axis.

Solution:

When a point (x, y) is reflected in the Y-axis, the new coordinates become (-x, y).

(a) A(1,2) → A'(-1,2)

(b) M(2,3) → M'(-2,3)

(c) C(4,5) → C'(-4,5)

(d) D(6,6) → D'(-6,6)

(e) E(5,4) → E'(-5,4)

(f) F(2,5) → F'(-2,5)

(g) G(9,8) → G'(-9,8)

(h) H(3,9) → H'(-3,9)

3. Reflect the point P(5,-6) in Y-axis. A) Find the co-ordinates of P'.

Solution:

Finding P'

Reflection in the Y-axis changes (x, y) to (-x, y).

So, P(5, -6) → P'(-5, -6).

B) Find the length of PP'.

Solution:

Finding the length of PP'

The distance between a point and its reflection in the Y-axis is given by:

Distance = |x1 - x2|

Substituting the values:

Distance = |5 - (-5)| = |5 + 5| = 10

So, the length of PP' is 10 units.

4. P (4, 3), Q (7, 3) and R (4, -3) are the vertices of a right angled triangle. Draw the triangle and its image in the graph paper after reflecting in y-axis.

Solution:

Here,

P (4, 3), Q (7, 3), and R (4, -3) are the vertices of a right angled triangle ΔPQR.

After reflecting ΔPQR in the Y-axis, the new coordinates of the reflected image ΔP'Q'R' are:

P' (-4, 3), Q' (-7, 3), and R' (-4, -3).

5. A (2, -2), B (8, 3) and C (5, -2) are the vertices of a triangle. Draw the triangle and its image in the graph paper after reflecting in Y-axis.

Solution:

Here,

A (2, -2), B (8, 3), and C (5, -2) are the vertices of a triangle ΔABC.

After reflecting ΔABC in the Y-axis, the new coordinates of the reflected image ΔA'B'C' are:

A' (-2, -2), B' (-8, 3), and C' (-5, -2).

6. Plot A (-2, 3), B (-5, 2) and C (-4, 5) in graph paper and then find the image ΔA'B'C' after reflecting about Y-axis. Again, reflect the final image ΔA'B'C' with Y-axis and present in the graph paper.

Solution:

Here,

A (-2, 3), B (-5, 2), and C (-4, 5) are the vertices of a triangle ΔABC.

After reflecting ΔABC in the Y-axis, the new coordinates of the reflected image ΔA'B'C' are:

A' (2, 3), B' (5, 2), and C' (4, 5).

Again, reflecting ΔA'B'C' in the Y-axis, the final image ΔA''B''C'' has coordinates:

A'' (-2, 3), B'' (-5, 2), and C'' (-4, 5).

Rotation

Exercise 19.3

1. Plot the following points in graph and rotate each points centre about origin through 90°.

Solution:

Rotation by 90° counterclockwise

Each point (x, y) transforms to (-y, x).

Original Point (x, y) → New Point (-y, x)

a. (-4,7) → (-7,-4)

b. (4,-7) → (7,4)

c. (5,9) → (-9,5)

d. (3,0) → (0,3)

e. (-4,-8) → (8,-4)

f. (2,-5) → (5,2)

g. (10,-10) → (10,10)

h. (0,6) → (-6,0)

i. (0,0) → (0,0)

j. (-9,-9) → (9,-9)

2. Plot the following points in graph and rotate each points centre about origin through -90°.

Solution:

Rotation by -90° (90° clockwise)

Each point (x, y) transforms to (y, -x).

Original Point (x, y) → New Point (y, -x)

a. (-4,7) → (7,4)

b. (4,-7) → (-7,-4)

c. (5,9) → (9,-5)

d. (3,0) → (0,-3)

e. (-4,-8) → (-8,4)

f. (2,-5) → (-5,-2)

g. (10,-10) → (-10,-10)

h. (0,6) → (6,0)

i. (0,0) → (0,0)

j. (-9,-9) → (-9,9)