Write a rule in function notation to describe the transformation that is a reflection across the x-axis.

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Write a rule in function notation to describe the transformation that is a reflection across the x-axis.

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Khải Quang 3 years 2021-08-25T05:41:25+00:00 1 Answers 2 views 0

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  1. mit
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    2021-08-25T05:42:47+00:00
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    Answer:

    R(x, y) = (x, -y)

    Step-by-step explanation:

    When we have a reflection across some line, the distance between the original point and the reflected point to the line is invariant.

    For a reflection around the x-axis, the x-value is invariant, then the only value that can change is the y-value.

    So if we have a point like (4, 7)

    Which is at a distance of 7 units to the x-axis, the only other point that is also at a distance of 7 units to the x-axis that has the same x-value is (4, -7)

    Here we already can see the rule.

    If we have a point (x, y), the reflection across the x-axis gives us the point (x. -y)

    Then we can write this reflection as a function in the next way:

    R(x, y) = (x, -y)

    This means that if the input is the point (x, y), the output is the point (x, -y)

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