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Reflection over the -axis is a type of geometric transformation that moves every point on an object to a new position. Imagine the -axis as a mirror. Every point will have an image on the opposite side of the -axis at the same distance from the -axis.
If a point is reflected over the -axis, its image's coordinates, , will follow the rule:
Thus, the image of point is .
Note that the value of the -coordinate does not change, while the value of the -coordinate becomes its opposite (negative if positive, positive if negative).
Suppose we have point . If point is reflected over the -axis, its image, , can be determined as follows:
The original -coordinate is , so .
The original -coordinate is , so .
Thus, the image of point is .
Let's visualize this:
Now, let's reflect a triangle with vertices , , and over the -axis.
To reflect a triangle, we need to reflect each of its vertices.
By connecting the image points , we obtain the reflected triangle.
Suppose we have a line with the equation . To find the equation of its image after reflection over the -axis, we substitute with (because ) and with (because ) into the original equation.
Original equation:
Substitute :
The equation of the image is:
Let's visualize these two lines:
The image of point is .
Explanation: , .
The coordinates of the image triangle are:
The equation of the image of the line is .
Substitute with into the original equation:
The equation of the image of the line is .
Explanation: Substitute with :
