PROBLEMS ON REFLECTION OVER Y EQUALS X

The rule of reflection about y = x is

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

What is preimage ?

Preimage In a transformation, the original figure is called the preimage.

What is image ?

Image In a transformation, the final figure is called the image.

Reflections can be performed easily in the coordinate plane using the general rules below.

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)