PROBLEMS ON REFLECTION ACROSS THE Y AXIS

Graph the image of the figure using the transformation given.

Problem 1 :

Solution :

Marking the point U (2, -3). Reflection of U across y-axis is

U’ (-2, -3)

Problem 2 :

Reflection across the y-axis

Y (2, 2)

Solution :

Marking the point Y (2, 2). Reflection of Y across y-axis is

Problem 3 :

Reflection on y-axis

Solution : 

Marking the point K (2, -2). Reflection of K across y-axis is

K’ (-2, -2)

Problem 4 :

Solution :

By observing the figure, coordinates of the vertices are

C (1, -1), E (0, -1), M (3, -3) and W (1, -3)

C (1, -1) ==> C’ (-1, -1)

E (0, -1) ==> E’ (0, -1)

M (3, -3) ==> M’ (-3, -3)

W (1, -3) ==> W’ (-1, -3)

Problem 5 :

Reflection across y-axis

Solution :

By observing the figure, coordinates of the vertices are

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

W (-4, 0) ==> W’ (4, 0)

I (-1, -1) ==> I’ (1, -1)

X (-3, -5) ==> X’ (3, -5)

Problem 6 :

Reflection across the y-axis

D (-2, -3), E (2, -2) and F (3, -4)

Solution :

Rule:

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

D (-2, -3) ==> D’ (2, -3)

E (2, -2) ==> E’ (-2, -2)

F (3, -4) ==> F’ (-3, -4)

Problem 7:

Solution:

By observing the figure, coordinates of the vertices are

I (4, 0), J (0, 2), K (-2, -1) and L (0, -3)

I (4, 0) ==> I’ (-4, 0)

J (0, 2) ==> J’ (0, 2)

K (-2, -1) ==> K’ (2, -1)

L (0, -3) ==> L’ (0, -3)

Problem 8:

Reflection across the y-axis

J (-2, -4), K (-3, -1), L (-1, -1), M (2, -5)

Solution:

Rule:

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

J (-2, -4) ==> J’ (2, -4)

K (-3, -1) ==> K’ (3, -1)

L (-1, -1) ==> L’ (1, -1)

M (2, -5) ==> M’ (-2, -5)

Problem 9 :

The vertices of a rectangle are A(−4, −3), B(−4, −1), C(−1, −1), and D(−1, −3).

a. Draw the rectangle and its reflection in the x-axis.

b. Draw the rectangle and its reflection in the y-axis.

c. Are the images in parts (a) and (b) the same size and shape? Explain.

Solution :

a) Rule for reflection across x-axis

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

A(−4, −3) ==> A'(-4, 3)

B(−4, −1) ==> B'(-4, 1)

C(−1, −1) ==> C'(-1, 1)

 D(−1, −3) ==> D'(-1, 3)

a) Rule for reflection across y-axis

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

A(−4, −3) ==> A'(4, -3)

B(−4, −1) ==> B'(4, -1)

C(−1, −1) ==> C'(1, -1)

 D(−1, −3) ==> D'(1, -3)

c. Yes, after reflection the shapes are congruent.

Problem 10 :

The vertices of a quadrilateral are P(−2, 5), Q(−1, −1), R(−4, 2), and S(−4, 4). Draw this quadrilateral and its reflection in the y-axis. What are the coordinates of the image?

Solution :

P(−2, 5), Q(−1, −1), R(−4, 2), and S(−4, 4)

Reflection across y-axis :

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

P (−2, 5) ==> P' (2, 5)

Q (−1, −1) ==>Q' (1, -1) 

R (−4, 2) ==> R' (4, -2)

S (−4, 4) ==> S' (4, 4)

Problem 11 :

Given the point (3, 4), find its reflection over the x-axis.

Solution :

Reflection across x-axis :

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

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

Problem 12 :

Given the point (3, 4), find its reflection over the y-axis.

Solution :

Reflection across y-axis :

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

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

Problem 13 :

For the function f(x) = 2x - 3, graph both f(x) and its reflection over the x-axis on the same set of axes.

Solution :

f(x) = 2x - 3

Reflection over the x-axis :

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

-y = 2x - 3

y = -2x + 3

Problem 14 :

Point P is first reflected in x-axis to P′. P′ is then reflected in y-axis to P′′(–2, 5). The coordinates of P are:

(a) (2, 5)      (b) (–2, –5)      (c) (2, –5)      (d) (–5, 2)

Solution :

To find the point P, we have to work backwards.

After reflections done, we get the point P''(-2, 5)

Reflecting this point with respect to y-axis,

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

P''(-2, 5) ==> P'(2, 5)

Going back, reflection across x-axis,

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

P'(2, 5) ==> P(2, -5)

So, option c is correct.

Problem 15 :

The vertices of a triangle are A (−1, 1), B (2, 3), and C (6, 3). Draw this triangle and its reflection in the x-axis. What are the coordinates of the image?

Solution :

Reflection across x-axis,

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

A (−1, 1) ==> A'(-1, -1)

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

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