Question

Find the coordinates of the image after a reflection in the given line.
[-8, 1, -7]
[-7, -5, 1]; y axis

Answer 1

@dan815 can you help me sir?

Answer 2

What does a reflection about an axis mean? If they are reflected about an axis they should still have the same distance from that access right? If a point is located as following (ignore the z-component): Then the point is reflected about the axis. More generally for any point (a, b, c). A reflection about any axis means that the distance from that axis must be preserved. The only possible orientation for a point to have such that it remains the same total distance is its reflection.

For any point P (a, b, c):
about x: (-a, b, c)
about y: (a, -b, c)
about z: (a, b, -c)

note* these are the only possible values such that a point would be equally distant from an axis as before, while maintaining a different orientation such that the rotation is only about the given axis.

Answer 3

oh sry didnt see this

Answer 4

Did I do it right? @cdosborn
\[\left[\begin{matrix}8 & -1 & 7\\ -7 & -5 & 1\end{matrix}\right]\]

Answer 5

No, make a list of the points, then perform the operation on each point into a new list and comment. I'm not sure what you did to get the above.

Answer 6

It depends if you have two 3 dimensional points, or three 2 dimensional points.

Answer 7

Ok so I have:
[-8, 1, -7]
[-7, -5, 1]

The points would be: because (x, y)?
-8, -7
1, -5
-7, 1

Now what do I do?

Answer 8

I should apologize, I misspoke about the point (a,b,c) reflected about the x,y,z axis. Ignore that part. However, to reflect a point about an axis, its distance from that axis must be the same, but the point must be in a new location.

For a point (a, b):
reflected about the x axis: = (a, -b)
about the y axis: = (-a, b)

Plot some sample points and see that these are the only possible values to preserve the one defining quality of a reflected point about an axis, that it remain an equal distance from that axis in a different orientation