![reflection over y axis reflection over y axis](https://www.onlinemath4all.com/images/exploringreflections2.png)
∴ Co- ordinates of the point P' are (2k - x, y). Since, M is the mid- point of the line segment PP', then by mid- point formula, Then P' is the image of P after reflection in the line x = k.
![reflection over y axis reflection over y axis](https://showme0-9071.kxcdn.com/files/239777/pictures/thumbs/602157/last_thumb1357612749.jpg)
Draw a perpendicular PM from P to the line x = k and produce it to the point P' such that PM = MP'. So, the reflection in a line parallel to Y- axis means reflection in the line x = k.
![reflection over y axis reflection over y axis](https://pixnio.com/free-images/2017/05/31/2017-05-31-23-49-15.jpg)
The equation of a line parallel to Y- axis is given by x = k where k is X - intercept of the line.
![reflection over y axis reflection over y axis](https://i.ytimg.com/vi/8uh2_jQ-rMk/maxresdefault.jpg)
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. Find a point on the line of reflection that creates a minimum distance.A reflection is a transformation that flips a figure across a line.Determine the number of lines of symmetry.Describe the reflection by finding the line of reflection.Where should you park the car minimize the distance you both will have to walk? You need to go to the grocery store and your friend needs to go to the flower shop. Now we all know that the shortest distance between any two points is a straight line, but what would happen if you need to go to two different places?įor example, imagine you and your friend are traveling together in a car. And did you know that reflections are used to help us find minimum distances?