Point $P(-2,5)$ is reflected on the line $y=\frac{2}{5}x$. How do you find the coordinates of the reflection using linear algebra and not the distance formula?
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1Possible duplicate of Linear Algebra with Reflection – Oct 31 '18 at 15:30
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Rotate, reflect across the $x$-axis, rotate back. – amd Nov 01 '18 at 04:02
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The vector representing the slope of the line is $\overrightarrow{m}=(run,rise)=(5,2)$. The vector representing the point is $\overrightarrow{P}=(-2,5)$
Notice that $\overrightarrow{P}$ is perpendicular to $\overrightarrow{m}$, so the vector $\overrightarrow{P}$ gives us the distance from $P$ to the line.
In particular, reflection of the point P is given by $$-\overrightarrow{P}=(2,-5)$$
(draw the picture and you will see why this works)
NazimJ
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That would be a reflection, but I'm not sure how you reflect it over the line y=2/5x – Madison Oct 31 '18 at 15:30
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Because the 2 vectors I mention are perpendicular, it is the reflection over the line. Please draw the picture and you should see it – NazimJ Oct 31 '18 at 16:13