 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that describe the sequence of transformation that results in transform of triangle ABC to triangle A prime B prime C prime. Let us move on to the solution. In this question we are given a triangle ABC and its transformation emerged if triangle A prime B prime C prime. If we compare the two images we see that triangle ABC is rotated at 90 degrees in clockwise direction with center as origin. Then it will shift from second quadrant to first quadrant. Now if we see reflection of rotated image in x axis then it will be of shape that is given in fourth quadrant. Also the size is reduced it means figure is dilated with scale factor line between 0 and 1. So we say that first time the figure is rotated then reflected and then dilated. So first we find coordinates of A, B and C. From the figure it is clear that vertex A has coordinates minus 3, 1. Then vertex B has coordinates minus 2, 4 and vertex C has coordinates minus 1, 1. Therefore we can say in triangle ABC we have vertex A with the coordinates minus 3, 1. Vertex B with the coordinates minus 2, 4 and vertex C with the coordinates minus 1, 1. Now let us rotate it at 90 degrees with center at origin in clockwise direction. We know that any coordinates say x, y changes to y minus x when rotated at 90 degrees. So we can say A with the coordinates minus 3, 1 on rotation at 90 degrees in clockwise direction changes to 1, 3. Similarly B with the coordinates minus 2, 4 changes to 4, 2. And C with the coordinates minus 1, 1 changes to 1, 1. So we have a new triangle in first quadrant with vertices having coordinates 1, 3, 4, 2 and 1, 1. This is the rotated image of triangle ABC when rotated at 90 degrees in clockwise direction. Now we reflect this image in x axis. Now we know that any coordinates say x, y on reflection in x axis becomes x minus y, vertex A with coordinates 1, 3. On reflection in x axis becomes 1 minus 3, vertex B with coordinates 4, 2. On reflection in x axis becomes 4 minus 2. Similarly vertex C with coordinates 1, 1 on reflection in x axis becomes 1 minus 1. Now we shall plot these points on the graph and hence we get the reflected triangle in the fourth quadrant. Now from the given figure we can see that coordinates of A prime are 0.5 minus 1.5. Similarly coordinates of vertex B prime are given by 2 minus 1 and C prime are 0.5 minus 0.5. That is we are given vertex A prime with the coordinates 0.5 minus 1.5 B prime with the coordinates 2 minus 1 and C prime with the coordinates 0.5 minus 0.5. If we compare these coordinates with the coordinates of vertices A, B and C after reflection in x axis we can say that these coordinates are multiplied by half which will be the scale factor reflected image is dilated using 1 by 2 As scale factor hence we get the triangle A prime B prime C prime with A prime having coordinates 0.5 minus 1.5 B prime with the coordinates 2 minus 1 and C prime with the coordinates 0.5 minus 0.5. So these three transformations of rotation, reflection and dilation are used to obtain triangle A prime B prime C prime. This completes our session. Hope you enjoyed this session.