![]() ∴ Co- ordinates of the point P' are (x, 2k - y). Since, M is the mid-point of the line segment PP', then by mid- point formula, Let thye co- ordinates of P' be (x', y'). Then P' is the image of P after reflection in Draw a perpendicular PM from P to the line y = k and produce it to the point P' such that PM = PM'. So, reflection in the line parallel to X- axis means reflection in the line y = k. The equation of a line parallel to X- axis is given by y = k where k is Y- intercept of the line. Reflection in the line parallel to X- axis.Hence, if R y denotes the reflection in Y- axis, then: ∴ Image of point P(x, y) after reflection in Y- axis P' (-x, y). ∴ Co- ordinates of the point P' are (-x, y). Since M is the mid-point of line segment PP', then by mid- point formula, Then P' is the image of P after reflection in Y- axis. ![]() Draw a perpendicular PM from the point P to the Y- axis and produce it to the point P' such that PM = MP'. So, reflection in Y- axis means reflection in the line x = 0. Hence, if R x denotes the reflection in X- axis, then:Įquation of Y- axis is x = 0. ∴ Image of point P(x, y) after reflection in X- axis is P'(x, -y). Since L is the mid- point of line segment PP', then by mid- point formula, Then P' is the image of P after reflection in X- axis. Draw a perpendicular PL from the point P to the X- axis and produce it to the point P' such that PL = LP'. So, reflection in X- axis means reflection in the line y = 0. In reflection, the object figure and its image figure are congruent to each other.Įquation of X- axis is y = 0. The points on the axis of reflection are invariant points.į. XX'is perpendicular bisector of AA', BB' and CC' as in fig 3.ĭ. The lines joining the same ends of the object and image are perpendicular to reflecting axis.Īxis of reflection is the perpendicular bisector of the line segment joining same ends of object and image. ![]() It means top remains at the top, bottom remains at the bottom but left side goes to the right side and right side goes to the left side as shown in fig 2.Ĭ. The shape of objects and images are laterally inverted. ![]() Coordinates can be used for finding images of geometrical figures after the reflection in the lines like X- axis, Y- axis, a line parallel to X- axis, a line parallel to Y- axis, the line y = x, the line y = -x, etc.The distance of the object from the axis of reflection is equal to the distance of reflection is equal to the distance of the image from the axis is a reflection.ī. When geometrical figures are reflected in the axis of reflection, the following properties are found.Ī. Characteristics of reflection of geometrical figures in the axis. The mirror line is also called the axis of reflection. It means the mirror line is perpendicular bisector of the line segment joining object and image. The line work as a plane mirror. In reflection, the line joining the object and the image is perpendicular to the mirror line. When you reflect a point in the origin, both the x-coordinate and the y-coordinate are negated (their signs are changed).A reflection is a transformation that flips a figure across a line. 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. Assume that the origin is the point of reflection unless told otherwise. 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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