 Hello and welcome to this session. In this session we will discuss reflection. First of all we define reflection. Reflection is the type of transformation in which a figure is reflected across a line which is called the axis of reflection or the mirror line we can say the reflection line fixed mirror in A the other side axis of reflection denotes the operation reflect with this M is the reflection line or you can say the axis of reflection or the mirror line we also call it the mediator if we have a reflection line M and if the image of two reflection we write it as R M such that P goes to P dash that is P dash is the image of P after reflection in the line M or we can also write this as of P is equal to P dash as P dash is the image of P so P is the point P dash. Now next let us see how we can the image of a point after reflection suppose we need to find P to reflection consider this point P we have to find the image of this point P after reflection of this line M so for this what we do is we mark a point on the other side of the reflection line M and this point should be at the same distance between the line M and the point P should be same as the distance between the line M and the point P dash and also we have to make sure that the line segment joining the two points P dash is perpendicular to the reflection line. So this is the point P dash which is the point P after reflection in the line now with this point P so O P O P dash and also P P dash is perpendicular to the line that the point P lies on the reflection line M this means the image of the point P under the reflection in line M when the point P is on the reflection line M is point P itself. We can find the image of the triangle ABC after reflection in this line M by the same method take this triangle A dash B dash C dash as the image of triangle ABC under reflection in line M A dash is the image of point A after reflection in line M in the same way B dash and C dash are also images of points B and C respectively after reflection in line M so we also find that A dash B dash that is the line segment A dash B dash is the image of the line segment AB after reflection in the line M same as the case for the line segments A dash C dash and B dash C dash they are the images of the line segments B C and A C respectively after reflection in the line M we can find out the images of the quadrilateral after reflection in a given line with some properties related to reflection ABC height we have the vertex A dash but the original figure on the right hand side we had the point B and this A dash is not the image of point B but it is the image of the point A so this means the position of the triangle ABC is changed under reflection the next property figure is preserved after reflection a triangle would remain a triangle after reflection and a circle would remain a circle after reflection and so on for the other figures like you have this line segment AB the image of the line segment AB after reflection is A dash B dash this is also a line segment so this shows that the shape of the figure is preserved under reflection under reflection for this triangle ABC or you can say CDA clockwise ABC is A dash B dash C dash B dash A dash and here the sense of A dash that the sense or you can say the orientation of a figure is not preserved under reflection or we can say that if the original figure is described in counter clockwise sense when the image of the figure would be described in clockwise sense and vice versa the reflection and in the image figure would be same as the length of the line in the original figure like if you consider this the length of B dash which is the image of AB would be same as the length of AB so that the distance is preserved like if we have two lines AB and AC angle between these two lines is angle BAC and angle between the corresponding lines in the image that is in triangle A dash B dash C dash the corresponding lines are A dash B dash and A dash C dash and the angle between these two lines is angle B dash A dash C dash that is this angle and these two angles would be equal that is angle BAC would be equal to angle B dash A dash C dash although the sense is different that we have is the image of a figure would be same as the area of the original figure so in this case area of triangle A dash B dash C dash would be same as the area of triangle ABC next property is the points the points that lie on the middle line do not change by reflection so if we have a point say a point P on the middle line M point P is its own image next property that we have is parallelism means AB and CD A dash B dash and image of CD is C dash B dash and we observe that A dash B dash is parallel to C dash D dash so this shows that parallelism is preserved under reflection we can also see that between AB and CD is 0 degrees and so the angle between their images would also be 0 degrees that is between A dash B dash and C dash B dash would also be 0 degrees and so this is because we know that angle measure is preserved under reflection or the reflection line between the angle between this line A dash that is it bisects this angle so this means this angle would be equal to this angle that is angle so this mirror line bisects the angle between the line A and its image and dash that is it bisects angle this these two angles would be equal to the reflection the reflection which is a point after reflection and also the properties of reflection