WRITE A RULE TO DESCRIBE REFLECTION

Write a rule to describe each transformation.

Problem 1 :

Solution :

Comparing the corresponding coordinates of two shapes,

H(-3, -3) ==> H'(-1, -3)

I(-3, 1) ==> I'(-1, 1)

K(-5, -3) ==> K'(1, -3) 

There is no change in y-coordinates, by observing the triangles from -2 on the x coordinate

H and H' are at the same distance

K and K' are at the same distance

I and I' are at the same distance

So, there is vertical line of reflection and

line of reflection at x = -2

Problem 2 :

Solution :

Comparing the corresponding coordinates of two shapes,

G(2, 2) ==> G'(-2, 2)

X(3, 3) ==> X'(-3, 3)

F(4, 1) ==> F'(-4, 1) 

There is no change in y-coordinates, comparing x-coordinates, the signs alone is changed.

So,

reflection across y-axis.

Problem 3 :

Solution :

Comparing the corresponding coordinates of two shapes,

X(-2, 1) ==> X'(-2, 1)

N(-5, 4) ==> N'(1, 4)

Z(-3, 5) ==> F'(-1, 5) 

There is no change in y-coordinates, x coordinates are changed except X. So, there may be horizontal or vertical line of reflection.

From -2 on the x-coordinate N and N' are at the same distance. Z and Z' are at the same distance. Then, there is vertical line of reflection and it is 

reflection across x = -2

Problem 4 :

Solution :

Comparing the corresponding coordinates of two shapes,

S (3, -4) ==> S' (1, -4)

M (1, -2) ==> M' (-3, -2)

B (-1, -2) ==> B' (-5, -2)

U (-1, -3) ==> U' (-5, -3)

There is no change in y-coordinates, x coordinates are changed.

From 2 on the x-coordinate

• S and S' are at the same distance. 
• M and M' are at the same distance.
• B and B' are at the same distance.
• U and U' are at the same distance.

So,

reflection across x = 2

Problem 5 :

Solution :

Comparing the corresponding coordinates of two shapes,

Q (-1, 3) ==> Q' (-1, -1)

P (-2, -2) ==> P' (-2, 4)

S (3, 3) ==> S' (3, 5)

R (4, 2) ==> R' (-5, -3)

There is no change in x-coordinates, y coordinates are changed.

From 1 on the y-coordinate the vertical distance, so there may be horizontal reflection.

• Q and Q' are at the same distance. 
• P and P' are at the same distance.
• S and S' are at the same distance.
• R and R' are at the same distance.

So,

reflection across y = 1

Problem 6 :

L(0, 1), K(0, 2), J(3, 3), I(5, 1)

to

L'(0, -1), K'(0, -2), J'(3, -3), I'(5, -1)

Solution :

By comparing the corresponding coordinates

L (0, 1) ==> L' (0, -1)

K (0, 2) ==> K' (0, -2)

J (3, 3) ==> J' (3, -3)

I (5, 1) ==>  I' (5, -1)

There is no change in x-coordinate. (x, y) ==> (x, -y)

So,

Reflection across x-axis.

Problem 7 :

Find the coordinates of the figure after reflecting in the x-axis.

a) A (3, 2), B (4, 4), C (1, 3)

b) M(−2, 1), N(0, 3), P(2, 2)

c) H(2, −2), J(4, −1), K(6, −3), L(5, −4)

d) D(−2, −1), E(0, −2), F(1, −5), G(−1, −4)

Solution :

a) A (3, 2), B (4, 4), C (1, 3)

Reflection across x-axis :

(x, y) ==> (x, -y)

A (3, 2) ==> A' (3, -2)

B (4, 4) ==> B' (4, -4)

C (1, 3) ==> C' (1, -3)

b) M(−2, 1), N(0, 3), P(2, 2)

Reflection across x-axis :

(x, y) ==> (x, -y)

M (-2, 1) ==> M' (-2, -1)

N (0, 3) ==> N' (0, -3)

P (2, 2) ==> P' (2, -2)

c) H (2, −2), J (4, −1), K (6, −3), L (5, −4)

Reflection across x-axis :

(x, y) ==> (x, -y)

L (2, -2) ==> L' (2, 2)

J (4, -1) ==> J' (4, 1)

K (6, -3) ==> K' (6, 3)

L (5, -4) ==> L' (5, 4)

d) D(−2, −1), E(0, −2), F(1, −5), G(−1, −4)

Reflection across x-axis :

(x, y) ==> (x, -y)

D (-2, -1) ==> D' (-2, 1)

E (0, -2) ==> E' (0, 2)

F (1, -5) ==> F' (1, 5)

G (-1, -4) ==> G' (-1, 4)

Problem 8 :

Reflect the triangle in the line y = x. How are the x and y-coordinate of the image related to the x and y-coordinate of the original triangle ?

Solution :

The coordinates of the triangle are

D (-1, 3), E (-1, 1) and F (-3, 1)

Reflection across y = x

D (-1, 3) ==> D' (3, -1)

E (-1, 1) ==> E' (1, -1)

F (-3, 1) ==> F' (1, -3)