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Thread: reflection in the line y = x+1???

  1. #1
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    reflection in the line y = x+1???

    If the line y = 2x+3 is reflected in the line y = x+1, find what its equation becomes.
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  2. #2
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    Quote Originally Posted by usagi_killer View Post
    If the line y = 2x+3 is reflected in the line y = x+1, find what its equation becomes.
    When you reflect a line over $\displaystyle y = x$, you simply switch the x and y variables.

    So $\displaystyle y = 2x + 3$ becomes

    $\displaystyle x = 2y + 3$

    $\displaystyle 2y = x - 3$

    $\displaystyle y = \frac{1}{2}x - \frac{3}{2}$

    The resulting equation of a line is also known as the inverse of the original equation.

    In the problem, the line was reflected over $\displaystyle y = x + 1$, so you add $\displaystyle 1$ to the inverse of the original equation.

    $\displaystyle y = \frac{1}{2}x - \frac{3}{2} + 1$

    $\displaystyle y = \frac{1}{2}x - \frac{1}{2}$

    If you drew $\displaystyle y = 2x+3$ and $\displaystyle y = \frac{1}{2}x - \frac{1}{2}$ on graph paper and folded the paper at $\displaystyle y = x + 1$, the two lines should be right on top of each other.
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