 Hello and welcome to the session. In this session we will discuss the question which says that the vertices of triangle PQR are T with coordinates 6 minus 2, Q with coordinates 8 minus 4 and R with coordinates 3 minus 7. Reflects triangle PQR in the line x is equal to 2. The coordinates of triangle P dash QR dash in the line minus 4 finds the coordinates of triangle P double dash Q double dash R double dash which transformation would be same as this double reflection. Now let us start the solution of the given question. Now here we have given a triangle PQR with vertices P, Q and R. Now let us plot these points on the graph. Now here this is the point P with coordinates 6 minus 2, this is the point Q with coordinates 8 minus 4 and this is the point R with coordinates 3 minus 7. Now join P to Q, Q to P and now we have to reflect triangle PQR in the line. Let us draw the line x is equal to 2 to the vertical line which is parallel to the y axis and which cuts the x axis at the point 0. So this is the line x is equal to 2. Now we have to reflect the given triangle PQR in this line that is the line x. Now we know that in reflection the pre-image points and the corresponding image points are from the line of reflection and both points lie on same line segment. So we will use this condition to plot the image points. Now here we can see that point P is at a distance 1, 2, 3 from the line of reflection given by x is equal to 2. Now let us extend this line image of the point P from this line of reflection given by x is equal to 2 and that point that is the line L from this line that is the line x is equal to 2 horizontally to left. Now here it is 1, 2, 3 and 4 units. We will locate the image point on the line L. So this is the point P dash with coordinates that the pre-image point that is the point P and image point that is the point P dash from the line of reflection given by x is equal to 2 is L. Now let us draw point of the point Q. Now the point Q is at a distance from the line of reflection given by x is equal to 2. So we pass to the left from the line of reflection on the same line where point Q lies we will place a point Q dash with coordinates minus 4. Now you see point R is at a distance of 1 unit from the line of reflection we will count 1 unit to the left from the line of reflection R dash with coordinates 1 minus 7. Now join P dash to Q dash Q dagger in age in the line x is equal to 2 and now we have to reflect triangle P dash Q dash R dash equal to minus 4. Now this is the line it is a vertical at 0. Now here this is equal to 2. Now here we have to reflect triangle P dash Q dash R dash in the line x is equal to minus 4. Now here point P dash is at a distance from the line of reflection given by x is equal to minus 4. Here is the point R and this is the point P double dash with coordinates minus 6 minus 2. Now it is for point Q dash that point Q dash lies is equal to minus 8 will be the point of minus 4. Now with coordinates minus 9 minus 7. Now join P double dash to Q double dash. Now joining these points we obtain a triangle P double dash Q double dash R double dash R double dash triangle P Q R plus triangle P double dash Q double dash R double dash with the translation using translation rule x well transforms minus 12. Now we can also check our conclusion using the rule on the vertices of now we have the point P with coordinates now we will use point P using this transformation rule or you can say translation rule so let us put x is equal to 6 and y is equal to 2 in this translation rule then the point is 12 minus P double dash with coordinates minus 6 minus 2 point Q dash coordinates 8 minus 4 translation rule point Q with coordinates 8 minus 4 transforms to minus 9 minus 7 double dash. Now here you must note that the line x is equal to 2 and when the double refill panel lines change its translation of original figure and here you can see this is the triangle P double dash Q double dash R double dash of original figure that is the triangle P Q R. So that's the given question that's all for this session hope you all enjoyed the session.