REFLECTION OVER X AXIS

Problem 1 :

Reflection across the x-axis T(2, 2), C(2, 5), Z(5, 4), F(5, 0)

Solution :

Rule : 

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

T (2, 2)  ==> T' (2, -2)

C (2, 5)  ==> C' (2, -5)

Z (5, 4)  ==> Z' (5, -4)

F (5, 0)  ==>  F'(5, 0)

Graph the image of the figure using the transformation given

Problem 2 :

reflection across the x-axis

Solution :

By observing the figure, coordinates of the vertices are

I (-1, -1), X (-3, -5) and W (-4, 0)

I (-1, -1)  ==>  I' (-1, 1)

X (-3, -5)  ==>  X' (-3, 5)

W (-4, 0)  ==>  W'(-4, 0)

Problem 3 :

reflection across the x-axis 

Solution :

By observing the figure, coordinates of the vertices are

T (0, 2), R (2, -1) and I (4, -4)

T (0, -2)  ==>  T' (0, 2)

R (2, -1)  ==>  R' (2, 1)

I (4, -4)  ==>  I'(4, 4)

Problem 4 :

Reflection across the x-axis X (2, 2)

Solution :

Rule : 

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

Problem 5 :

reflection across the x-axis K (1, -2), L (2, -2), M (3, -4)

Solution :

Rule : 

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

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

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

M (3, -4) ==> M' (3, 4)

Problem 6 :

A point P has coordinates (–4, 7). What are its new coordinates after reflecting point P in the x-axis?

a) (–4, –7)  b)  (4, –7)     c) (–4, 7)       d) (4, 7)

Solution :

Reflection about x-axis,

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

(-4, 7) --> (-4, -7)

Problem 7 :

A point P has coordinates (–1, –8). What are its new coordinates after reflecting point P in the y-axis?

a) (1, 8)     b) (–1, 8)     c) (1, –8)     d) (–1, –8)

Solution :

Reflection about y-axis,

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

(-1, -8) --> (1, -8)

Problem 8 :

A point P has coordinates (2, –3). What are its new coordinates after reflecting point P in the y-axis?

a) (2, –3)       b) (–2, –3)    c) (2, 3)      d) (–2, 3)

Solution :

Reflection about y-axis,

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

(2, –3) --> (-2, -3)

Problem 9 :

A point P has coordinates (5, –6). What are its new coordinates after reflecting point P in the x-axis?

a) (5, –6)   b) (5, 6)   c) (–5, –6)   d) (–5, 6)

Solution :

Reflection about x-axis,

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

(5, -6) --> (5, 6)

Problem 10 :

A point P has coordinates (–2, 7). What are its new coordinates after reflecting point P in the x-axis?

a) (2, –7)     b) (–2, –7)     c) (–2, 7)     d) (2, 7) 

Solution :

Reflection about x-axis,

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

(-2, 7) --> (-2, -7)

Problem 11 :

What are the coordinates of the reflection image of P(7, 3) in the y-axis?

Solution :

Reflection about y-axis,

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

(7, 3) --> (-7, 3)

Problem 12 :

What are the coordinates of the reflection image of P(-6, 2) in the y-axis?

Solution :

Reflection about y-axis,

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

(-6, 2) --> (6, 2)

Problem 13 :

What are the coordinates of the reflection image of P(-5, -6) in the x-axis?

Solution :

Reflection about x-axis,

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

(-5, -6) --> (-5, 6)

Problem 14 :

What are the coordinates of the reflection image of P(-8, -1) in the x-axis?

Solution :

Reflection about x-axis,

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

(-8, -1) --> (-8, 1)

Problem 15 :

What are the coordinates of the reflection image of P(-2 , -5) in the y-axis?

Solution :

Reflection about y-axis,

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

(-2, -5) --> (2, -5)

Problem 16 :

Graph the image of the figure using the transformation given.

Reflection across the x-axis

Solution :

To follow the reflection across x-axis, we have to use the rule

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

L (0, 0) ==> L'(0, 0)

M (2, 0) ==> M'(2, 0)

A (-1, -3) ==> A'(-1, 3)

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

Problem 16 :

Graph the image of the figure using the transformation given.

Reflection across the x-axis

Solution :

To follow the reflection across x-axis, we have to use the rule

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

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

U(0, 3) ==> U'(0, -3)

T (0, -1) ==> T'(0, 1)

W (-4, 0) ==> W'(4, 0)

Problem 17 :

Graph the image of the figure using the transformation given.

Reflection across the x-axis

Solution :

To follow the reflection across x-axis, we have to use the rule

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

K(0, 4) ==> K'(0, -4)

L(5, 5) ==> L'(5, -5)

M(3, 1) ==> M'(3, -1)