PROBLEMS ON REFLECTION OVER Y EQUALS MINUS X

Graph the image of the figure using the transformation given

Problem 1 :

Reflection across y = -x.

Solution :

By observing the coordinates of the vertices of the triangle given above

X (0, 5), L (-3, 1) and U (-3, 5)

Rule for reflection across y = -x :

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

X (0, 5) ==> X’ (-5, 0)

L (-3, 1) ==> L’ (-1, 3)

U (-3, 5) ==> U’ (-5, 3)

Problem 2 :

Reflection across y = -x.

Solution :

By observing the coordinates of the vertices of the triangle given above

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

Rule for reflection across y = -x:

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

L (1, 2) ==> L’ (-2, -1)

G (3, 4) ==> G’ (-4, -3)

Q (4, -1) ==> Q’ (1, -4)

Problem 3 :

Reflection across the line y = -x

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

Solution :

Rule for reflection across y = -x:

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

T (2, 2) ==> T’ (-2, -2)

C (2, 5) ==> C’ (-5, -2)

Z (5, 4) ==> Z’ (-4, -5)

F (5, 0) ==> F’ (0, -5)

Problem 4 :

Reflection across y = -x.

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

Solution :

Rule for reflection across y = -x :

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

H (-1, -5) ==> H’ (5, 1)

M (-1, -4) ==> M’ (4, 1)

B (1, -2) ==> B’ (2, -1)

C (3, -3) ==> C’ (3, -3)

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 :

a) By plotting the points A and B, we get

b) Reflection should be done across x-axis,

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

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

c) The horizontal distance between the point B and the line of reflection AA' is 2 units to the left. So, we have to move the same 2 units towards to the right from the line of reflection.

4 + 3 ==> 7

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

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

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 :

a)

b) Reflection should be done on y-axis.

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

D is the reflection of B on y-axis, then 

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

c) ABOD is a quadrilateral.

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 :

a) Plotting the points in the coordinate plane.

b) Reflection should be done on the y-axis :

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

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

B (4, –6) ==> B'(-4, -6)

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

c)

d) The shape is hexagon.

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 :

Rx (x, y) = (x, –y)

Ro (x, y) = (–x, y)

so, we have

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

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

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 :

(a) Rx (3, –2) ==> (3, 2)

(b) Ry (3, –2) ==> (–3, –2)

(c) Ro (3, –2) ==> (–3, 2)