If a function that passes through the origin maps onto itself after being reflected over the y-axis and the x-axis, it is an odd function.
Put another way, even functions are symmetric about the y-axis. Reflect the part on the right to the left of the line, and then reflect the part on the left of the line onto the right side.Īny function that passes through the y-axis and maps to itself when reflected over the y-axis is an even function.
In that case, the two sides of the object are treated separately. What happens when an object passes through the given line? For example, you can reflect an object over the x-axis and then the y-axis.
#Reflection in the y axis series
Note that we can use more than one line in a series of reflections. The Line of ReflectionĪny line can be a line of reflection, but the axes and the line through the origin with slope 1 are most common. If you pick up the original and flip it over onto the backside while moving it over the given line, you will have the reflected version’s orientation. To visualize the reflected version of an object, imagine a cut-out of the object sitting on a table. Put another way, the midpoint between any two corresponding points in the original image and the reflected image lies on the line of reflection. If the original figure is further from the line, the reflected figure will also be further from the line.
If the original figure is close to the line, the reflected figure will also be close to the line. The final figure will be an equal distance from the line as the preimage but on the opposite side. The most frequently used lines are the y-axis, the x-axis, and the line $y=x$, though any straight line will technically work.Ī reflection reverses the object’s orientation relative to the given line. Often, this line is the x-axis, y-axis, or the line $y=x$.īefore moving on, make sure to review math transformations and coordinate geometry.Ī reflection in geometry is a mirror image of a function or object over a given line in the plane. Reflection in Geometry – Explanation, and ExamplesĪ reflection in geometry is the transformation of an object by creating a mirror image of it on the other side of a given line.
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