 Hello and welcome to the session. In this session, we will discuss a question which says that identify the dilution and find its scale factor, then find the values of the variables. Now before starting the solution of this question, you should know some results. The dilution with centre C at scale factor k is a transformation that maps every point p in the play to a point p dash so that the following properties are true. First is the image of centre C is point C itself and the image of point other than centre say p has image p dash such that p dash will lie on line Cp and Cp dash is equal to absolute value of k times Cp and k is not equal to 1. Now the dilution is a reduction if absolute value of k lies between 0 and 1 and the dilution is enlargement if absolute value of k is greater than 1. Now these results will work out as a key idea for solving out the given question. And now let us start with the solution of the given question. Now in this figure we are given C as the centre, 3-image that is the triangle Jtm and dilated image that is the triangle J dash k dash m dash. Now in dilution the image and 3-image are similar. So here triangle Jtm is similar to triangle J dash k dash m dash. Now since these two triangles are similar so their correspondence sites are proportional. So we have T dash J dash upon Kj is equal to T dash m dash upon Km is equal to J dash m dash upon Jm. Now if K is the same factor then we know that ratio T dash J dash upon Kj is equal to T dash m dash upon Km is equal to J dash m dash upon Jm is equal to K. Now here we are given that dash m dash is equal to 28 and Km is equal to 14. And also here we can see that K dash m dash upon Km is equal to K. Now these values here K dash m dash that is 28 upon Km that is 14 is equal to K and this implies K is equal to 2. Thus same factor K is equal to 2 which is greater than 1. So it is an enlargement of the given figure. Now we can find the values of x and y using this equation let it be equation 1. Now from equation 1 we have K dash J dash upon Kj is equal to K. Now this implies and here you can see K dash J dash upon Kj is x is equal to K which is equal to 2. And this implies x is equal to 16 upon 2 which is equal to 8. Let us find the value of y. Now again from equation 1 we have J dash m dash upon Jm is equal to K. Now this implies the way you can see J dash m dash is 32 upon Jm is equal to y and this is equal to K that is the scale factor which is equal to 2. And this further implies y is equal to 32 upon 2 which is equal to 16. So we have x is equal to 8 and y is equal to 16. So this is the required answer and this completes our session. Hope you all have enjoyed this session.