Question

In your own words, explain how reflections across x-axis and across y-axis each affect the coordinates of the points of a figure.

Answer 1

Using reflections concepts, it is found that:

• When a function is reflected across the x-axis, the x-coordinates stay the same, while the y-coordinates will have the opposite signal.
• When a function is reflected across the y-axis, the y-coordinates stay the same, while the x-coordinates will have the opposite signal.

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The rule for a reflection across the x-axis is:

$(x,y) \rightarrow (x, -y)$

That is, the x-coordinates stay the same, while the y-coordinates will have the opposite signal.

For a reflection across the y-axis, the rule is:

$(x,y) \rightarrow (-x,y)$

That is, the y-coordinates stay the same, while the x-coordinates will have the opposite signal.

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