 Hello and welcome to the session. In this session we will discuss reflection in intersecting lines and in axis. First of all let us discuss reflection over axis. Now we have two axis that is x axis and y axis. We will contribute to each other. Now we will find what happens when we reflect a figure in y axis followed by the reflection of obtained image in x axis. Now here we have a triangle A, B, C. We have first reflected it in y axis using the transformation where the coordinates x, y are transformed to the coordinates minus x, y. So here the point A with coordinates x, y is transformed to the point A dash with coordinates minus x, y and we have obtained triangle A dash, B dash, C dash as the image of the given triangle ABC. Now again we have reflected this obtained image in x axis using transformation where the coordinates x, y are transformed to the coordinates x minus y. So here the point A dash with coordinates minus x, y is transformed to the point A double dash with coordinates minus x, minus y. And here we have got the triangle A double dash, B double dash, C double dash. And now carefully see the triangle ABC and triangle A double dash, B double dash, C double dash. And we see that triangle A double dash, B double dash, C double dash is a rotated image of triangle ABC at 180 degrees about origin because when a figure is rotated at 180 degrees about origin then we use the transformation where the coordinates x, y are transformed to the coordinates minus x, minus y. And here also coordinates of original figure are x, y and coordinates of this transformed figure are minus x, minus y which means this is a rotated image of the original figure at 180 degrees about origin. Thus we compose two reflections over each axis then the final image is the rotated image of original figure at 180 degrees about origin. And here you must note that order does not matter. We can also reflect in x-axis first followed by reflection in y-axis. So reflection in intersecting lines. Now a figure is reflected in two intersecting lines then final image is the rotation of the figure about the point of intersection of the two lines between the intersecting lines. Now suppose we have any two intersecting lines and now we draw a quadrilateral A, B, C, D on the side of one of the lines say M just reflect the quadrilateral in the line M and then we draw a perpendicular from the points A, B, C and D reflection. So we mark the image point A dash such that of reflection M to mark these points we have C dash and since we get a quadrilateral A dash, B dash, C dash, D dash this quadrilateral is the image of the quadrilateral A, B, C, D about the line. Now the second line now taking M as line of reflection we plot the image points of A dash, B dash, C dash and D dash in the similar way double dash, B double dash and D double dash thus is quadrilateral A double dash, B double dash, C double dash, D double dash. Now if we see the original figure and final image we see that final image is rotation of the original image about the point of in all with the help of protector v-nasir the angle of intersection at point B and here 90 degrees the angle between the two images for this we will take our original vertex now here let us take our original vertex B and its image point which is B double dash that is the final image point now from these two points meeting at point B. Now using protector let us measure the angle B, P, B double dash 180 degrees that is angle B, P, B double dash is 180 degrees so here angle B, P, B double dash is 180 degrees which means angle of rotation of the image is 180 degrees at point B is 90 degrees this means angle of rotation of the image is twice the angle that is the angle at the point affecting lines now if degrees then into it now we can easily find which is equal to two into angle of intersection that is 30 degrees and this is equal to 60 degrees. So in this session we have discussed reflection in intersecting line of view all have enjoyed the session