![]() So, the reflection in a line parallel to Y- axis means reflection in the line x = k. The equation of a line parallel to Y- axis is given by x = k where k is X - intercept of the line. Reflection in the line parallel to Y- axis.Hence, if R denotes the reflection in the line y = k, then: ∴ Image of point P (x, y) after reflection in the line y = k is P' (x, 2k - y). ∴ 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. In a translation, every point of the object must be moved in the same direction and for the same distance.A reflection is a transformation that flips a figure across a line. Notation Rule A notation rule has the following form ry−axisA → B = ry−axis(x,y) → (−x,y) and tells you that the image A has been reflected across the y-axis and the x-coordinates have been multiplied by -1. To write a rule for this reflection you would write: rx−axis(x,y) → (x,−y). Subsequently, question is, how do you write a reflection Rule? Both angles are measured with respect to the normal to the mirror. the angle of incidence i = the angle of reflection r. the incident ray, the reflected ray, and the normal to the surface of the mirror all lie in the same plane. Īdditionally, what are the two rules of reflection? The Laws of Reflection state: !. The rule for a reflection over the x - axis is ( x,y)→( x,−y). Reflection in the x - axis: A reflection of a point over the x - axis is shown. What is the rule for a reflection across the X axis? The rule for reflecting over the X axis is to negate the value of the y-coordinate of each point, but leave the x-value the same.Īlso asked, what is the rule for reflection over the x axis?
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