Rochester City School District / Overview



ReflectionsA reflection can be seen in water, in a mirror, or in a shiny surface.? An object and its reflection have the same shape and size, but the figures face in opposite directions.? In a mirror, for example, right and left are reversed.In mathematics, the reflection of an object is called its image.? If the original object (the preimage) was labeled with letters, such as polygon ABCD, the image may be labeled with the same letters followed by a prime symbol, A'B'C'D'.The line of reflection is the perpendicular bisector of the segment joining every point and its image.Reflections in the Coordinate PlaneReflecting over the x-axisWhen you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate is transformed into its opposite.?The reflection of the point (x, y) across the x-axis is the point (x, -y).Px, y→P'(x, -y) or rx-axisx, y=(x, -y)Reflecting over the y-axisWhen you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is transformed into its opposite.?The reflection of the point (x, y) across the y-axis is the point (-x, y).Px, y→P'(-x,y) or ry-axisx, y=(-x, y)Reflecting over the line y = xWhen you reflect a point across the line y = x, the x-coordinate and the y-coordinate change places.?Px, y→P'(y,x) or ry=xx, y=(y, x)Reflecting over any other lineNotice how each point of the original figure and its image are the same distance away from the line of reflection (x = –2 in this example).Reflecting over a pointA point reflection exists when a figure is built around a single point called the center of the figure, or point of reflection.? 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.? Under a point reflection, figures do not change size. Reflecting over the originA point reflection across the origin is the same as rotating a figure 180°, thus the figure is turned upside down. Px, y→P'(-x, -y) or roriginx, y=(-x, -y) ................
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