If you complete a glide reflection to the point H( -2, -3) with the translation (x , ) = ( x -2, y) and a reflection over y = -4.

find the point H.

huh???

glide: (x,y) -> (x-2,y)

reflection: (x,y) -> (x,-y-8)
so,
(-2,-3) -> (-4,-3) -> (-4,-5)

Oh, I see you've encountered some geometry jargon. Don't worry, I'm here to help!

Let's break it down step by step:

1. Start with the point H(-2, -3).
2. First, perform the glide reflection using the translation (x, y) = (x - 2, y). This means we'll shift the point horizontally to the right by 2 units. So, the new point becomes H'(-2 + 2, -3) = H'(0, -3).
3. Next, perform a reflection over the line y = -4. Since the line is horizontal, the y-coordinate of the point remains the same, while the sign of the x-coordinate changes. So, the new point becomes H''(0, -3).
4. Therefore, the final point after both transformations is H''(0, -3).

There you have it! The point H is (0, -3). Hope this clears things up with a touch of humor along the way!

To understand and solve the problem, let's break it down step-by-step.

Step 1: Understanding glide reflection
A glide reflection is a transformation that involves a reflection followed by a translation. In this case, we are given two transformations: a reflection over the line y = -4 and a translation (x, y) = (x - 2, y).

Step 2: Reflection over y = -4
To reflect a point over a horizontal line, we keep the x-coordinate the same and negate the y-coordinate. So, reflecting the point H(-2, -3) over y = -4 results in H'(-2, 1).

Step 3: Translation (x, y) = (x - 2, y)
To perform a translation, we shift the x-coordinate by -2 and leave the y-coordinate unchanged. Applying the translation to the point H'(-2, 1), we get H''((-2 - 2), 1), which simplifies to H''(-4, 1).

Step 4: Finding the final point H
The final point after performing the glide reflection is H''(-4, 1).

Therefore, the point H is (-4, 1).

To find the point H after performing a glide reflection, we need to go through the following steps:

Step 1: Apply the translation (x, y) = (x - 2, y) to the point H(-2, -3).
When you perform a translation, you move each coordinate a certain distance according to the given translation values. In this case, you subtract 2 from the x-coordinate.

Applying the translation to the x-coordinate of H, we get:
x' = -2 - 2 = -4

Since the y-coordinate remains the same, y' = -3.

So, after the translation, the point H' becomes (-4, -3).

Step 2: Apply the reflection over the line y = -4 to the transformed point H'.
When reflecting a point over a horizontal line, the y-coordinate remains the same, while the x-coordinate changes sign.

Since the line of reflection is y = -4, the y-coordinate of H' remains the same, y' = -3.

Now, we need to find the new x-coordinate by reflecting the x-coordinate of H' = -4.
x'' = -(-4) = 4.

So, after the reflection, the point H'' becomes (4, -3).

Therefore, the final position of the point H after performing the glide reflection is H''(4, -3).