Question

ABC with coordinates (1.3), B.4.5), and C15,2), what are the coordinates of ABC after the glide reflection described by t (-1,1) R y-axis?

Answer 1

A'(0,4)

B'(-3,6)

C(-4,3)

Explanation:

A glide reflection is the combination of a translation with a rotation.

In this question:

T(-1,1): This means that the translation is given by:

(x,y) -> (x-1,y+1)

Rotation: Around the y-axis. This means that:

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

The triangle has the following coordinates:

A(1,3), B(4,5), C(5,2)

Applying the translation:

(x,y) -> (x-1,y+1)

A(1,3) -> (1-1,3+1) = (0,4)

B(4,5) -> (4-1,5+1) = (3,6)

C(5,2) -> (5-1, 2+1) = (4,3)

Rotation over the y-axis:

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

A'(0,4)

B'(-3,6)

C(-4,3)