PROBLEMS ON REFLECTION OVER THE X AXIS

Find the coordinates of the vertices of each figure after the given transformation.

Problem 1 :

Reflection across x axis.

Solution :

By observing the figure, coordinates of the vertices are

B (-3, -1), W (-4, 2), Y (-1, 1) and Z (-2, 3)

B (-3, -1) ==> B’ (-3, 1)

W (-4, 2) ==> W’ (-4, -2)

Y (-1, 1) ==> Y’ (-1, -1)

Z (-2, 3) ==> Z’ (-2, -3)

Problem 2 :

Reflection across x axis.

Solution :

By observing the figure, coordinates of the vertices are

V (-1, 5), R (-3, 3) and C (0, 0)

V (-1, 5) ==> V’ (-1, -5)

R (-3, 3) ==> R’ (-4, -3)

C (0, 0) ==> C’ (0, 0)

Problem 3 :

Reflection across x axis.

Solution :

By observing the figure, coordinates of the vertices are

R (-3, 2), Z (0, 2), Y (2, -2) and J (-1, -3)

R (-3, 2) ==> R’ (-3, -2)

Z (0, 2) ==> Z’ (-4, -2)

Y (2, -2) ==> Y’ (-1, 2)

J (-1, -3) ==> J’ (-2, 3)

Problem 4:

Reflection across x 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 5 :

Reflection across x axis.

Solution :

By observing the figure, coordinates of the vertices are

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

R (2, -1) ==> R’ (2, 1)

T (0, -2) ==> I’ (0, 2)

I (4, -4) ==> X’ (4, 4)

Problem 6 :

Reflection across x axis.

Solution :

Making the point T (-4, 3). Reflection of T across x-axis is

T’ (-4, -3)

Problem 7 :

Reflection across x axis.

Solution:

Making the point K (2, -2). Reflection of K across x-axis is

K’ (2, 2)

Problem 8 :

Reflection across the x-axis

K (1, -2) L (2, -2) and 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 9 :

Reflection across the x-axis

A (-1, -5), B (-2, -2), C (-1, 0) and D (3, -2)

Solution :

Rule:

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

A (-1, -5) ==> A’ (-1, 5)

B (-2, -2) ==> B’ (-2, 2)

C (-1, 0) ==> C’ (-1, 0)

D (3, -2) ==> D’ (3, 2)

Problem 10 :

Graph △ABC with vertices A(3, 2), B(6, 3), and C(7, 1) and its image after the glide reflection.

Translation: (x, y) → (x − 12, y)

Reflection: in the x-axis

Solution :

A(3, 2), B(6, 3), and C(7, 1)

Given translation rule is that, moving the shape 12 units to the left and no movement vertically.

A(3, 2) ==> A'(3 - 12, 2) ==> A'(-9, 2)

B(6, 3) ==> B'(6 - 12, 3) ==> B'(-6, 3)

C(7, 1) ==> C'(7 - 12, 1) ==> C'(-5, 1)

Problem 11 :

Determine whether the coordinate plane shows a reflection in the x-axis, y-axis, or neither

Solution :

Coordinates of original figure :

A(-2, -1), B(-1, -1) and C(-2, -5)

Coordinates of new figure :

D(2, -1), E(1, -1) and F(2, -5)

A(-2, -1) ==> D(2, -1)

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

C(-2, -5) ==> F(2, -5)

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

The above rule should be followed when reflection across y-axis.

Problem 12 :

Determine whether the coordinate plane shows a reflection in the x-axis, y-axis, or neither

Solution :

Coordinates of original figure :

A(-2, 1), B(-1, 2) and C(-2, 3)

Coordinates of new figure :

D(1, 0), E(2, -1) and F(1, -3)

By observing the coordinates, we dont find any relationship between the coordinates. So, there is no reflection.

Problem 13 :

Graph triangle with vertices A(-1, 4) B(2, -1) and C(4, 3) and its image after the glide reflection.

Translation (x, y) ==> (x + 2, y - 1)

Reflection : in the line y = x

Solution :

Given that the translation of 2 units to the right and 1 unit down and reflection across the line y = x.

Order of transformation is, first reflection and then translation.

Before and after reflection :

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

Problem 14 :

Graph triangle with vertices A(-1, 4) B(2, -1) and C(4, 3) and its image after the glide reflection.

Translation (x, y) ==> (x - 3, y + 1)

Reflection : in the line y = -x

Solution :

Given that the translation of 2 units to the left  and 1 unit up and reflection across the line y = x.

Order of transformation is, first reflection and then translation.

Before and after reflection :

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