 Hello and welcome to the session. In this session we are going to discuss the following question which says that using the transformation xy transforms to x-5 y plus 4, the first part of the question says find the image of point a with the coordinates minus 5, 3. Second part is find the image of the point b with the coordinates 3 minus 4 and the third part is what is the image of point b prime and the fourth part says what is the pre-image of the point c prime with the coordinates 2, 7. Now let us start with the solution of this question. We are given a transformation function that is xy transforms to x-5 y plus 4. Now in the first part of the question we need to find image of point a having coordinates minus 5, 3. We make use of given transformation function to find its image. It means any coordinate given by xy transforms to x-5 y plus 4. So here we have xy is equal to minus 5, 3 and if we put x is equal to minus 5 and y is equal to 3 in the given transformation we get minus 5, 3 transforms to minus 5, minus 5, 3 plus 4 that is we have substituted the value of x as minus 5 and the value of y as 3 which is equal to minus 5, minus 5 that is minus of 10, 3 plus 4 that is 7. So we say that minus 5, 3 transforms to minus 10, 7 Thus we say that image of point a with the coordinates minus 5, 3 is point a prime with the coordinates minus 10, 7. Now we move on to the second part of the question. Where we have to find the image of point b with the coordinates 3 minus 4 that is we are given point b with the coordinates 3 minus 4 and we have to find image at this point. So we put the value of x as 3 and the value of y as minus 4 in the given transformation rule that is xy transforms to x minus 5 by plus 4. So here we get 3 minus 4 transforms to 3 minus 5, minus 4 plus 4 and we get 3 minus 5 with minus 2, minus 4 plus 4 is 0. So we say that 3 minus 4 transforms to minus 2, 0. Thus we say that image of point b with the coordinates 3 minus 4 is given by the point b prime with the coordinates minus 2, 0. Now the third part of the question says what is the image of point b prime? Now here we have to find image of the point b prime. In the second part of the question we have found image of point b with the coordinates 3 minus 4 is given by the point b prime with the coordinates minus 2, 0. That is coordinates of point b prime are minus 2, 0. And now we shall find its image using the given transformation rule. So here we put the value of x as minus 2 and the value of y as 0 in this transformation rule and therefore we get xy that is minus 2, 0 transforms to x minus 5 that is minus 2 minus 5, y plus 4 that is 0 plus 4 which is equal to minus 7, 4. So we say that image of point b prime with the coordinates minus 2, 0 is given by the point b prime with the coordinates minus 7, 4. Now we move on to the fourth part of the question which says what is the free image of the point c prime with the coordinates 2, 7? That is here we are given a point c prime with the coordinates 2, 7 and we need to find its free image that is we need to find the coordinates of point c using this transformation rule. And in this transformation rule we see that the free image coordinates are given by xy and image coordinates are given by x minus 5, y plus 4. So we have image that is x minus 5, y plus 4 is equal to 2, 7 and we need to find free image that is point c with the coordinates xy. Now equating the x and y coordinates we get x minus 5 is equal to 2 and y plus 4 is equal to 7 which implies that Now adding 5 on both the sides we get x is equal to 2 plus 5 and here subtracting 4 from both the sides we get y is equal to 7 minus 4 which implies that x is equal to 2 plus 5 that is 7 and y is equal to 7 minus 4 that is 3. So we have coordinates xy as 7, 3 thus we say that free image of point c prime with the coordinates 2, 7 is given by the point c with the coordinates 7, 3 which is the required answer. This completes our session. Hope you enjoyed this session.