REFLECTION OVER Y EQUAL X OR MINUS X WORKSHEET

Graph the image of the figure using the transformation given

Problem 1 :

Reflection over y = x.

Solution

Problem 2 :

Reflection over 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 the line y = x

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

Solution

Problem 5 :

Plot the points A (–2, 0), B (4, 0), C (1, 4) and D (–2, 4) on a graph paper.

Point D is reflected about the line x = 1 to get the image E.

Write the coordinates of E. Name the figure ABED.

Solution

Problem 6 :

Use graph paper for this question:

(a) The point P(2, 3) is reflected in the line x = 4 to the point P′. Write the coordinates of P′.

(b) Find the image of the point Q(1, –2) in the line x = –1.

Solution

Problem 7 :

Use graph paper for this question :

Find the coordinates of the image of (3, 1) under reflection in x-axis followed by reflection in the line x = 1.

Solution

Problem 8 :

Use graph paper for this question:

Points A and B have coordinates (2, 5) and (0, 3) respectively.

Find

(a) the image A' of A under reflection in x-axis.

(b) the image B' of B under reflection in the line AA'.

Solution

Answer Key

1)  X’ (5, 0), L’ (1, -3), U’ (5, -3)

2)  L’ (2, 1), G’ (4, 3), Q’ (-1, 4)

3)  T’ (2, 2), C’ (5, 2), Z’ (4, 5), F’ (0, 5)

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

5) A(-2, 0)  ==> A'(4, 0)

B (4, 0) ==> B' (-2, 0)

C (1, 4) ==> C' (1, 4)

D (2, 4) ==> D' (0, 4)

6) P(2, 3) ==> P'(6, 3)

Q'(-3, -2)

7) (-1, 1)

8) a) A (2, 5) ==> A' (2, -5)

b) B' (4, 3)

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’ (-5, 0), L’ (-1, 3), U’ (-5, 3)

2)  L’ (-2, -1), G’ (-4, -3), Q’ (1, -4)

3)  T’ (-2, -2), C’ (-5, -2), Z’ (-4, -5), F’ (0, -5)

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

5) 

a)

b) 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) 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) The shape is hexagon.

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)