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Find the reflection of $1 + i$ through the line $l$ with endpoints $3$ and $9$.

My approach:

Let AB be a line l with endpoints $(3,0)$ and $(9,0)$. Then, the line l lies along the x-axis so the image of the point $(x, y)$ becomes $(x, -y)$.

So we get $1-i$ as the image of $P(0, 1+i) -> P(0, 1-i)$

Is my approach right, or am I doing something wrong?

mathwizz123
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  • If the second endpoint is $(0,9)$, then the line does not lie along the x-axis. – Andreas Tsevas Dec 02 '21 at 02:01
  • @Andreas sorry edited, meant (9,0) – mathwizz123 Dec 02 '21 at 02:09
  • Then it looks correct to me. – Andreas Tsevas Dec 02 '21 at 02:10
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    Since you have the tag [hyperbolic-geometry] and mention endpoints of lines on the real axis, I assume you're working in the Poincaré half-plane model of the hyperbolic plane, in which case $l$ looks like a semicircle with midpoint $6+0i$, and $1-i$ is definitely not the correct solution since it's not in the upper half-plane. Now how to proceed likely depends on how reflections were defined in your course material and which geometric properties you know about the half-plane model. – Magma Dec 02 '21 at 13:44

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