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# Coordinates

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Let B be the reflection of A over the line $y = \frac{1}{2} x + 2$.  Find the coordinates of B.

May 7, 2022

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AB is perpendicular to the line y = 1/2 x + 2. So the slope of AB is -2.

Equation of AB is just y - 1 = -2(x - 3), which is 2x + y - 7 = 0.

The intersection of 2x + y - 7 = 0 and y = 1/2 x + 2 can be found via solving the system of linear equations $$\begin{cases}2x + y - 7 = 0\\y =\dfrac12x + 2\end{cases}$$.

The intersection point is (2, 3) and that's the midpoint of AB. Can you continue from here?

May 8, 2022