Question

For exercises 13-17, given the points A(-6, -4), B(3, 8), and C(-7, 9), determine the coordinates of the vertices A'B'C' for each glide reflection.

Answer 1

To determine the coordinates of the vertices A'B'C' for each glide reflection, we need to apply the glide reflection transformation to the given points A(-6, -4), B(3, 8), and C(-7, 9).

Step-by-step explanation:

To determine the coordinates of the vertices A'B'C' for each glide reflection, we need to apply the glide reflection transformation to the given points A(-6, -4), B(3, 8), and C(-7, 9).

A glide reflection involves reflecting the points across a line of reflection and then translating them along the same line. To perform the glide reflection, we first reflect each point across a line of reflection. Then, we translate the reflected points along the same line.

Let's say the line of reflection is given by the equation y = mx + b. We can find the transformed coordinates by following these steps:

1. Find the reflected points by using the formula x' = (x - 2 * ((mx + b) - y)) / (m^2 + 1) and y' = mx' + b.
2. Find the translation vector by subtracting the original coordinates from the reflected coordinates: x'' = x' - x and y'' = y' - y.
3. Add the translation vector to the reflected coordinates to find the transformed coordinates: x''' = x'' + x' and y''' = y'' + y.

Repeat these steps for each of the points A, B, and C to find the coordinates of the vertices A'B'C'.