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When you reflect a point in the origin, both the x-coordinate and the y-coordinate are negated (their signs are changed). Imagine a straight line connecting A to A' where the origin is the midpoint of the segment. Triangle A'B'C' is the image of triangle ABC after a point reflection in the origin. The y value of the new coordinate will always be the opposite of the y value of the pre-image and the x value will always remain constant because the figure does not move left or right, but instead, is flipped to the opposite side of the x-axis. The important part of the formula is the expression on the right hand side. Coordinate rule: (x, -y) The coordinate rule (x, - y) will hold for any shape reflected over the x-axis. 1 x y reflect across the x axis translate left units 2 x y. To reflect over a vertical line, such as x a x a, first translate so the line is shifted to the y-axis, then reflect over it, then translate back so the line is shifted to its original position. Assume that the origin is the point of reflection unless told otherwise. Reflection Over The X-Axis: Sets of Coordinates. In the table below, there are two y-coordinates for the x-coordinate -10. While any point in the coordinate plane may be used as a point of reflection, the most commonly used point is the origin. Under a point reflection, figures do not change size or shape. ![]() For every point in the figure, there is another point found directly opposite it on the other side of the center such that the point of reflection becomes the midpoint of the segment joining the point with its image. By looking through the plastic, you can see what the reflection will look like on the other side and you can trace it with your pencil.Ī point reflection exists when a figure is built around a single point called the center of the figure, or point of reflection. The Mira is placed on the line of reflection and the original object is reflected in the plastic. You may be able to simply "count" these distances on the grid.Ī small plastic device, called a Mira ™, can be used when working with line reflections. Notice that each point of the original figure and its image are the same distance away from the line of reflection.
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