I give an alternative derivation using complex variables as well. What Should a Reflection Do? We expect a reflection across a line $\ell$ to leave $\ell$ fixed in the plane and take the line …

Reflecting a function along the line y = x is the same as computing the inverse of the function. So use a method for computing the inverse of a function to find the reflection about the line y = x.

Sep 7, 2023 · Consider the reflection matrix: $$\begin {bmatrix} 0 & 1 \\ 1 & 0 \\ \end {bmatrix}$$ This matrix reflects a point over the y = x axis. Now consider a point on a function, (x,f (x)). …

Jan 8, 2017 · The premise was to use a arbitrary line perpendicular to the parallel lines to obtain points of intersection that would be used in the midpoint formula to get a point within the …

Jan 22, 2016 · To reflect over a vertical line, such as $x=a$, first translate so the line is shifted to the y-axis, then reflect over it, then translate back so the line is shifted to its original position.

27 How can I find the coordinates of a point reflected over a line that may not necessarily be any of the axis? Example Question: If P P is a reflection (image) of point (3, −3) (3, 3) in the line 2y …

Oct 7, 2019 · Suppose the two functions whose graphs are reflections over the line $y=x$ are named $f$ and $g$. What does it even mean to say the graphs are reflections over the line …

Oct 31, 2013 · 1 If you were to fold the graph on the line you're reflecting through, the original shape and the reflected shape should line up exactly. This could apply to any line: vertical, …

Aug 13, 2024 · I'm working on a geometric problem involving reflections and need help finding two lines. Specifically, I have a point $(x, y)$, and I want to reflect it across two lines such that after …

Apr 13, 2020 · 0 In 3-space, there is an elaborate theory of reflections about planes but you can also reflect about a line or a point.