 Hello and welcome to the session. In this session we will discuss how we can find a translated image using reflection and glide reflection. Till now we have discussed performing a single transformation i.e. translation or reflection or rotation. Now we will see how can we perform more than one transformation for a given figure. Now a transformation made up of successful transformations is called a computation. Now let us discuss translation by repeated reflections. Now we can find the translation of a given figure by performing a reflection in the first of two parallel lines and reflecting the obtained image again in the other parallel lines. Now suppose we have given a quadrilateral ABCD and we want to find its translated image using sequence of reflections. Now here let us draw a line M. We first reflect the given figure in line M and we get a quadrilateral A-B-C-D and this is reflected image of the given figure. Now we again reflect the image A-B-C-D in the line N which is parallel to the line M. Now quadrilateral A-B-C-D is the new reflected image of quadrilateral A-B-C-D and if we compare the two quadrilaterals that is given figure which is the quadrilateral A-B-C-D and the final image which is the quadrilateral A-B-B-C-D. We see that quadrilateral A-B-B-C-D is a translation of quadrilateral A-B-C-D thus we can obtain a translated image by reflecting the figure successively in two parallel lines and now let us discuss light reflection. Now a light reflection is the compilation of the plane that consists of a line of reflection and a translation in the direction of the line of reflection defined in even order. Now let us have a triangle A-B-C having vertices A with coordinates 1, 2, B with coordinates 5, 3 and C with coordinates 3, 4. Now we want to reflect this triangle in Y-axis on the quadrilateral plane. Now for reflection in Y-axis we have the transformation where X-Y transforms to minus X, Y. Now the given triangle has vertices A with coordinates 1, 2, B with coordinates 5, 3 and C with coordinates 3, 4. Now we have to reflect these vertices in Y-axis so using this transformation vertex A with coordinates 1, 2 transforms to vertex A- with coordinates minus 1, 2. Vertex B with coordinates 5, 3 transforms to vertex B- with coordinates minus 5, 3. Vertex C with coordinates 3, 4 transforms to vertex C- with coordinates minus 3, 4. Now let us plot these points on the coordinate plane. Now when we plot these points on the coordinate plane we get image which is given by triangle A-B-C- which is the image of triangle A-B-C when reflected in Y-axis. Now we know that a glide reflection is the composition of the plane that consists of a line of reflection and a translation in the direction of the line of reflection. Now here we have reflected triangle A-B-C in Y-axis. Now we translate the reflected image using the transformation where XY transforms to X-0, Y-4 where A is 0 and B is minus 4 in the transformation where XY transforms to X plus A, Y plus B which is a translation. So using this translation that is this translation we will translate triangle A-B-C- Now we have vertex A- with coordinates minus 1, 2, vertex B- with coordinates minus 5, 3 and vertex C- with coordinates minus 3, 4. Now using this translation vertex A- with coordinates minus 1, 2 transforms to vertex A- with coordinates minus 1, minus 0 that is minus 1, 2 minus 4 that is minus 2. Similarly using this translation vertex B- with coordinates minus 5, 3 transforms to vertex B- with coordinates minus 5, minus 0 that is minus 5, 3 minus 4 that is minus 1. Similarly vertex C- with coordinates minus 3, 4 transforms to vertex C- with coordinates minus 3, 0. Now let us plot these points on the coordinate plane. So here we have plotted all three points on the coordinate plane and we get a triangle A-B-C- So triangle A-B-C- is translated to triangle A-B-C- And triangle A-B-C- is the final image. So this type of composition of the plane that consists of a line of reflection and a translation in the direction of the line of reflection is called light reflection. Now you must know that we have to translate in the direction of line of reflection given the y-axis. Since y-axis is vertical so translation will also be vertical that is why we do not move horizontal in translation. So we have taken x minus 0 that is A is equal to 0. Thus vertical line the translation will be up or down to reflect over a horizontal line then the translation will be left or right. Also glide reflection preserves distance so it is an isometric. Now in glide reflection order does not matter. We can reflect the figure followed by a translation or we can translate first followed by reflection. Now in this example we have reflected the original image in y-axis followed by a translation. We can also do translation first followed by reflection. In both these cases we will get triangle A-B-C- as final image. So order does not matter in glide reflection. So in this session we have discussed how we can find a translated image using reflection and glide reflection. And this completes our session. Hope you all have enjoyed the session.