Question

Write a rule for the glide reflection that maps ABC with vertices A(-4,-2), B(-2, 6).

and C(4, 4) to A'B'C' with vertices A'(4, -2), B(6, -6), and C'(12,-4).

Answer 1

The glide reflection is a combination of a reflection and a translation. To find the rule, determine the reflection axis and the translation vector. The rule is a reflection over the x-axis followed by a translation of (8, 0).

Step-by-step explanation:

The glide reflection is a combination of a reflection and a translation. In order to find the rule, we need to determine the reflection axis and the translation vector.

Step 1: Find the reflection axis by finding the midpoint of the corresponding vertices in ABC and A'B'C'. The midpoint of A and A' is (-4 + 4)/2 = 0, so the x-axis will be the reflection axis.

Step 2: Find the translation vector by subtracting the coordinates of the corresponding vertices in ABC and A'B'C'. Taking A to A' as an example, A' = A + m, where m is the translation vector. So, (4, -2) = (-4, -2) + m, which gives us m = (8, 0).