 Hello and welcome to the session. In this session we will discuss a question which says that draw the dilated image of trapezoid PQRS with center C and k that is scale factor is equal to minus 3. Now before starting the solution of this question we should know some results. Calculation with center C scale factor k is a transformation that maps every point P in the plane to a point P dash so that the following properties are true. And first property is the image of center C point C itself and second property is the image of point other than center say P Cp dash is equal to absolute value of k into Cp and k is not equal to 1 is reduction is less than absolute value of k is less than 1 that is f is between 0 and 1 enlargement negative then the image lies opposite to the center of pre-image. Now these results will work out as a key solving out the given question. Now let us start with the solution of the given question trapezoid k is equal to minus 3 we are given is equal to minus 3 is negative to the center of pre-image scale factor k is minus 3 which is negative so image to the center of pre-image to 3 and 3 is greater than 1 we know that dilation is enlargement value of k is equal to 3 which is greater than 1 so the image will be enlargement is not given so we are can be drawn easily. Now let us take the point C here now let us draw raise to the vertices of trapezoid point P then we have drawn point Q then we have drawn ray N from point C and passing to the point R from point C and passing to the point now here scale factor k is negative so we make the image no in dilation corresponding image point lie on same center so here let us see idea that is Cp dash is equal to absolute value of k into Cp now here is equal to now we have absolute value of k is equal to 3 so Cp dash is equal to 3 times Cp so we plot at length C is the length Cp which we put a dot which represents the point P dash such that length R dash and S dash such that is equal to 3 times C up is equal to 3 times C we will locate the point on the ray O dash we will locate the point trapezoid P dash Q dash R dash instead of the given question and that is all for this session hope you all have enjoyed the session.