∴ 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. That is, (x, y) (–x, y).A reflection is a transformation that flips a figure across a line. Use the horizontal grid lines to find the corresponding point for each vertex so that the y-axis is equidistant from each vertex and its image.
Reflect the object below over the y-axis: Name the coordinates of the original object: T T’ T: (9, 8) R: (9, 3) Y: (1, 1) R’ R Name the coordinates of the reflected object: Y’ Y T’: (-9, 8) R’: (-9, 3) Y’: (-1, 1) The x-coordinates opposite, the y-coordinates sameī' A' C' D' Quadrilateral ABCD has vertices Graph ABCD and its image under reflection in the y-axis. Reflect across the y-axis Change the sign of the x-value Use the vertical grid lines to find the corresponding point for each vertex so that the x-axis is equidistant from each vertex and its image. Graph ABCD and its image under reflection in the x-axis.
Reflect the object below over the x-axis: Name the coordinates of the original object: A A: (-5, 8) B: (-6, 2) D C C: (6, 5) D: (-2, 4) B Name the coordinates of the reflected object: A’: (-5, -8) B’ B’: (-6, -2) D’ C’: (6, -5) C’ D’: (-2, -4) A’ The x-coordinates same the y-coordinates opposite.ĭ' C' A' B' Quadrilateral ABCD. Reflect across the x-axis Change the sign of the y-value Orientationof the image of a polygon reflected is opposite the orientation of the pre-image (orientation – CW: clockwise CCW: Counter-clockwise) the line of reflection is the perpendicular bisector of the segment connecting two reflected points 3. pre-image and image are equidistant from the line of reflection 2.Coordinate Reflections - 1 Reflecting over the x-axis and y-axisģ squares from mirror line 3 squares from mirror line FLIP IT OVER! Original shape Reflected shape Mirror line Make sure the reflected shape is the same distance from the mirror line as the original shapeģ squares from mirror line 3 squares from mirror line E E FLIP IT OVER! Original shape Reflected shape Mirror line Make sure the reflected shape is the same distance from the mirror line as the original shape