Question

Point M with coordinates (4, 8) is translated along a glide reflection to its image of M' (-2, 6)

Which best describes the glide reflection?

Answer 1

A glide reflection is a type of transformation that involves both a translation and a reflection. In this case, point M with coordinates (4, 8) is translated to its image M' (-2, 6) through a glide reflection.

Step-by-step explanation:

A glide reflection is a type of transformation that involves both a translation and a reflection. In this case, point M with coordinates (4, 8) is translated to its image M' (-2, 6) through a glide reflection. Here's how the glide reflection works:

1. First, determine the translation vector by finding the difference between the coordinates of M and M', which is (-6, -2).
2. Next, reflect the translated point along the line of reflection. The line of reflection can be found by taking the midpoint of the original point and its image, which is ((4+(-2))/2, (8+6)/2) = (1, 7).
3. Finally, apply the translation vector to the reflected point to obtain the final image M', which is (1-6, 7-2) = (-5, 5).

In summary, the glide reflection that maps point M(4, 8) to its image M'(-2, 6) involves a translation of (-6, -2) and a reflection over the line (1, 7).