 Hello and welcome to the session. In this session we are going to discuss the following question which says that reflect the given figure in the line y is equal to x. We know that reflection flips the figure over a line to create a mirror image and transformation rule for reflection in line y is equal to x is given by xy transforms to yx and this result will work out as the key idea to solve the given question. Now on the question we are given a triangle line in the third quadrant and we need to reflect this given triangle in the line y is equal to x. Now let us start with the solution of the given question. Now first of all we shall label the vertices of the triangle as a, b and c. Next we find the coordinates of the vertices that is vertex a has coordinates minus 6 minus 4, vertex b has coordinates minus 8 minus 8 and vertex c has coordinates minus 2 minus 6. Next we draw a line which is given by the equation y is equal to x. Now y is equal to x is a straight line passing through origin. Now let us plot any two points lying on this line using input output method that is when we put the value of x as 1 we get y is equal to 1 and when x is equal to 2 y is also equal to 2. Similarly when the value of x is minus 2 then also y is equal to minus 2. So we plot these points on the graph and join them and then we extend the line on both sides. Now this line represents the equation of the line that is y is equal to x and we need to reflect this given triangle in the line y is equal to x that is this line. Now in the next step we shall find image points of the vertices a, b and c using the transformation rule for reflection in line y is equal to x that is xy transforms to yx. So image point of vertex a with the coordinates minus 6 minus 4 is given by the point a prime with the coordinates minus 4 minus 6. Similarly image point of vertex b with the coordinates minus 8 minus 8 is given by the point b prime with the coordinates minus 8 minus 8 and image point of vertex c with the coordinates minus 2 minus 6 is given by the point c prime with the coordinates minus 6 minus 2. And now we shall plot these points on the coordinate plane so now we have plotted these points on the coordinate plane that is point a prime with the coordinates minus 4 minus 6 point b prime with the coordinates minus 8 minus 8 and point c prime with the coordinates minus 6 minus 2 and here we see that the coordinates of point b and its image are same that is minus 8 minus 8 and they lie on the line of reflection that is y is equal to x. So we say that whenever a point lies on the line of reflection its image is that point itself and in the next step we join point a prime to point b prime, point b prime to point c prime and point c prime to point a prime. So we have the reflected image of the triangle a b c as triangle a prime b prime c prime in the line y is equal to x. So this is the required image of the given triangle. This completes our session. Hope you enjoyed this session.