Question

After a glide reflection, the point x is mapped to the point x' (3,-2). The translation part of the glide reflection is (x,y) ->(x+3,y), and the line of reflection is y=-1. What are the coordinates of the original point x.

Answer 1

The coordinates of the original point x, can be obtained by reversing the given transformations individually

The coordinates of the original point x is $\underline{(0, \, 0)}$

Reason:

The type of reflection = Glide reflection

Coordinates of the image of the point x = x'(3, -2)

The translation part of the glide reflection is (x, y) → (x + 3, y)

The line of reflection is y = -1

The coordinates of the original point = Required

Solution:

• A glide reflection is also known as a transflection, that involves a symmetric composite transformation of a reflection followed by a translation along the line of reflection

Reflection part;

The distance of the image point from the reflecting line = The object's

point distance from the reflecting line

Therefore, given that the reflecting line is the line y = -1, and the image

point is x'(3, -2), we have;

Distance of image from reflecting line =-1 - (-2) = 1

∴ Distance of object point from reflecting line = 1

y-coordinate of object point = -1 + 1 = 0

Point of image of the object before reflection and after translation = (3, 0)

Translation part;

The translation of the glide reflection is (x, y) → (x + 3, y)

Therefore, the location of the object before translation is ((x + 3) - 3, y), which from the point (3, 0) gives, ;

((3) - 3, 0) → (0, 0)

The coordinates of the original point x is $\underline{(0, \, 0)}$

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