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What Is the Pre-image of Vertex A’ if the Rule That Created the Image Is Ry-Axis(X Y) → (–X Y)?
In mathematics, transformations play a crucial role in understanding the movement and changes of objects and shapes. One such transformation is a reflection, which involves flipping an object or shape across a specified line. In this article, we will explore the concept of a reflection and determine the pre-image of a vertex when a specific rule is applied.
The given rule for the reflection is Ry-Axis(X Y) → (–X Y). Let’s break down this rule to understand its meaning. “Ry-Axis” indicates that the reflection will occur across the y-axis. The (X, Y) signifies the coordinates of a point before the transformation, while (–X, Y) represents the coordinates after the reflection.
Now, let’s consider a specific vertex, A’, and determine its pre-image using the given rule. To find the pre-image, we need to reverse the transformation applied to A’ and determine the original position of the vertex.
Let’s assume that the coordinates of A’ after the reflection are (-3, 2). To find its pre-image, we reverse the reflection rule. Since the reflection occurred across the y-axis, we flip the x-coordinate and keep the y-coordinate unchanged. Therefore, the pre-image of A’ can be obtained by applying the rule Ry-Axis(X Y) in reverse, resulting in (3, 2).
In this case, the pre-image of vertex A’ is located at (3, 2) on the coordinate plane.
FAQs:
Q: What is a reflection in mathematics?
A: A reflection is a transformation that involves flipping an object or shape across a specified line. It results in mirroring the object or shape with respect to the line of reflection.
Q: What is a pre-image?
A: In mathematics, a pre-image refers to the original position or shape of an object or point before a specific transformation is applied. It is determined by reversing the given transformation to find the initial coordinates.
Q: How do we determine the pre-image of a vertex in a reflection?
A: To determine the pre-image of a vertex in a reflection, we need to reverse the transformation applied to the vertex. This can be done by applying the opposite operation of the given transformation rule.
Q: How does the given reflection rule Ry-Axis(X Y) → (–X Y) work?
A: The given reflection rule, Ry-Axis(X Y) → (–X Y), indicates that the reflection occurs across the y-axis. It means that the x-coordinate of a point is flipped or negated, while the y-coordinate remains unchanged.
Q: What is the significance of understanding transformations in mathematics?
A: Transformations are fundamental in mathematics as they help us analyze and manipulate shapes, objects, and functions. They provide insights into the behavior and changes of mathematical entities, enabling us to solve complex problems and understand various mathematical concepts.
In conclusion, the pre-image of vertex A’ can be determined by reversing the given reflection rule, Ry-Axis(X Y) → (–X Y). By applying this rule in reverse, we find that the pre-image of A’ is located at (3, 2) on the coordinate plane. Understanding transformations, such as reflections, is essential in mathematics as they allow us to analyze and manipulate shapes and objects, leading to a deeper understanding of mathematical concepts.
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