REFLECTION OVER HORIZONTAL AND VERTICAL LINES WORKSHEET

Problem 1 :

Reflection across y = -1

Solution

Problem 2 :

Reflection across y = -1

C (2, 0), D (5, 3), E (4, -1)

Solution

Problem 3 :

Reflection across y = -1

Q (-3, -4), R (-4, 0), S (-2, 0)

Solution

Problem 4 :

Reflection across x = -2

Q (-4, 1), R (-3, 5), S (0, 3), T (-3,-1)

Solution

Problem 1 :

Reflection across y = -1

R (-3, -5), N (-4, 0), V (-2, -1) E (0, -4)

Solution

Problem 2 :

Reflection across x = 3

F (2, 2), W (2, 5), K (3, 2)

Solution

Problem 3 :

Reflection across x = -1

V (-3, -1), Z (-3, 2), G (-1, 3), M (1, 1)

Solution

Problem 4 :

Reflection across x = 3

Solution

Problem 5 :

The points (3, 0) and (–1, 0) are invariant points under reflection in the line L1, while the points (0, –3) and (0, 1) are invariant points under reflection in the line L2.

(a) Name the lines L1 and L2

(b) Write down the images of the points P(3, 4) and Q(–5, –2) on reflection in L1. Name the images as P′ and Q′ respectively.

(c) Write down the images of P and Q on reflection in L2. Name the images as P′′ and Q′′ respectively.

(d) State or describe a single transformation that maps P′ onto P′′.

Solution

Graph the image of the figure using the transformation given

Problem 1 :

Reflection across y = -x.

Solution

Problem 2 :

Reflection across y = -x.

Solution

Problem 3 :

Reflection across the line y = -x

T (2, 2), C (2, 5), Z (5, 4), F (5, 0)

Solution

Problem 4 :

Reflection across y = -x.

H (-1, -5), M (-1, -4), B (1, -2), C (3, -3)

Solution

Problem 5 :

Use graph paper for this questions.

(a) Plot the points A (4, 6) and B (1, 2)

(b) A' is the image of A when reflected in x-axis.

(c) B' is the image of B when B is reflected in the line AA′.

(d) Give the geometrical name for the figure ABA′B′.

Solution

Problem 6 :

Use graph paper for this question. A(0, 3), B(3, –2) and O (0, 0) are the vertices of triangle ABO.

(a) Plot the triangle on a graph sheet taking 2 cm = 1 unit on both the axes.

(b) Plot D, the reflection of B in the y-axis, and write its co-ordinates.

(c) Give the geometrical name of the figure ABOD.

Solution

Problem 7 :

Use a graph paper to answer the following questions. (Take 1 cm = 1 unit on both axes)

(a) Plot A(4, 4), B(4, –6) and C(8, 0), the vertices of a triangle ABC.

(b) Reflect ABC on the y-axis and name it as A′B′C′.

(c) Write the coordinates of the image A′, B′ and C′.

(d) Give a geometrical name for the figure AA′C′B′BC.

Solution

Problem 8 :

A triangle with vertices A (1, 2), B (4, 4) and C (3, 7) is first reflected in the line y = 0 onto ∆A′B′C′ and then ∆A′B′C′ is reflected in the origin onto ∆A′′B′′C′′. Write down the co-ordinates of

(a) A′, B′ and C′

(b) A′′, B′′ and C′′.

Solution

Problem 9 :

Write down the coordinates of the image of the point (3, –2) when :

(a) reflected in x-axis.

(b) reflected in y-axis.

(c) reflected in the origin.

Solution

Answer Key

1)

X (0, 5) ==> X’ (-5, 0)

L (-3, 1) ==> L’ (-1, 3)

U (-3, 5) ==> U’ (-5, 3)

2)

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

L (1, 2) ==> L’ (-2, -1)

G (3, 4) ==> G’ (-4, -3)

Q (4, -1) ==> Q’ (1, -4)

3)

T (2, 2) ==> T’ (-2, -2)

C (2, 5) ==> C’ (-5, -2)

Z (5, 4) ==> Z’ (-4, -5)

F (5, 0) ==> F’ (0, -5)

4) 

H (-1, -5) ==> H’ (5, 1)

M (-1, -4) ==> M’ (4, 1)

B (1, -2) ==> B’ (2, -1)

C (3, -3) ==> C’ (3, -3)

a)

b) B (3, -2) ==> D (-3, -2)

c) ABOD is a quadrilateral..

5) a)

b)

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

A (4, 6) ==> A' (4, -6)

c)

B (1, 2) ==> B' (7, 2)

d) After plotting B' and joining the points together, we get the geometrical shape kite.

6) a)

b) B (3, -2) ==> D (-3, -2)

c) c) ABOD is a quadrilateral.

7) a)

b)

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

B (4, –6) ==> B'(-4, -6)

C (8, 0) ==> C' (-8, 0)

c)

d) 

8)

(a) A′ (1, –2), B′ (4, – 4) and C′ (3, –7)

(b) A′′ (–1, 2), B′′ (–4, 4) and C′′ (–3, 7)

9)

(a) Rx (3, –2) ==> (3, 2)

(b) Ry (3, –2) ==> (–3, –2)

(c) Ro (3, –2) ==> (–3, 2)