PROBLEMS ON REFLECTION OVER Y EQUALS X

Graph the image of the figure using the transformation given

Problem 1 :

Reflection over 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 over 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 the line 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 :

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 :

By plotting the given coordinates, we get

The horizontal distance between each point and the line of reflection,

A(-2, 0) :

The horizontal distance between A and x = 1 is 3 units towards the left, then we have to move the 3 units towards the right.

A'(4, 0)

B (4, 0) :

The horizontal distance between B and x = 1 is 3 units towards the right, then we have to move the 3 units towards the left.

B' (-2, 0)

C (1, 4) :

Since the point is on the line of reflection, so there is no change in the point C.

C' (1, 4)

D (2, 4) :

The horizontal distance between D and x = 1 is 1 unit towards the right, then we have to move the 1 unit towards the left.

D' (0, 4)

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 :

a)

The horizontal distance between P(2, 3) and the line of reflection x = 4 is 2 units to the left, to find the point of reflection, we have to move 2 units to the right from the line of reflection.

P(2, 3) ==> P'(6, 3)

(b) The horizontal distance between the point Q(1, –2) and the line of reflection x = –1 is 2 units to the right, so we have to move 2 units left from the line of reflection.

x = -1 - 2

Q'(-3, -2)

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 :

Given point is (3, 1),

the horizontal distance between the point and line of reflection x = 1 is 2 units towards right, so we have to move the same 2 units left from the line of reflection.

(3, 1) ==> (1 - 2, 1) ==> (-1, 1)

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 :

A (2, 5) and B (0, 3)

a) Reflection across x-axis :

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

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

B (0, 3)

The horizontal distance from (0, 3) to the vertical line is 2 units. From the line of reflection, we have to move 2 units to the right.

2 + 2 ==> 4

B' (4, 3)