Find the coordinates of the image after a reflection in the given line.

[-8, 1, -7]
[-7, -5, 1]; y axis

I am really bad with these types (matrices) of questions, please help me.

A

A
B
C 8 -1 7. -7 -5 1

Not sure what a 2x3 matrix has to do with coordinates. Can you splain a bit, please?

X is right 100% on quick check

Glad to hear that! Do you need any further assistance?

No worries, I'm here to help! Let's break it down.

To find the image after a reflection in the y-axis, we need to switch the sign of the x-coordinate while keeping the y and z coordinates the same.

So, if we have the coordinates (-8, 1, -7), after reflecting in the y-axis, the x-coordinate becomes positive 8, and the y and z coordinates remain the same. Therefore, the new coordinates are (8, 1, -7).

Hope that clarifies it for you! If you have any more questions, feel free to ask.

Of course, I'll be happy to help you with this question! To find the coordinates of the image after a reflection in a given line, you can follow these steps:

1. Identify the line of reflection. In this case, the line of reflection is the y-axis.

2. Determine the distance between each point and the line of reflection. To do this, you can draw perpendicular lines from each point to the line of reflection and find the length of these lines. Alternatively, you can consider that the line of reflection is represented by the equation x = 0, and find the distance between each point and this equation by calculating the x-coordinate of each point.

3. Flip the sign of the x-coordinate for each point to reflect it across the line of reflection. Since the line of reflection is the y-axis (x = 0), you simply need to change the sign of the x-coordinate. The y-coordinate remains the same.

Let's apply these steps to the given points:

Point 1: (-8, 1, -7)
To find the distance between this point and the y-axis (line of reflection), we can simply consider the x-coordinate of this point, which is -8.

To reflect this point across the y-axis:
- Change the sign of the x-coordinate to its opposite, so -8 becomes 8.
- Leave the y-coordinate and z-coordinate unchanged.

Therefore, the coordinates of the image after the reflection are (8, 1, -7).

Point 2: (-7, -5, 1)
Again, the distance between this point and the y-axis can be determined by considering the x-coordinate, which is -7.

To reflect this point across the y-axis:
- Change the sign of the x-coordinate to its opposite, so -7 becomes 7.
- Leave the y-coordinate and z-coordinate unchanged.

So, the coordinates of the image after the reflection are (7, -5, 1).

I hope this explanation helps! Let me know if you have any further questions.