 Hello and welcome to the session. In this session, we are going to discuss the following question which says that rotate the given figure by 270 degrees anti-clockwise about origin. Now we know that a rotation turns the figure around a point and transformation rule for rotating a figure at 270 degrees angle counterclockwise about origin is given by xy transforms to y-x. Now this result will work out as a key idea for the given question. Now let us start with the solution. Now in the question, we are given a triangle and we use a series of steps to rotate the given triangle by 270 degrees anti-clockwise about origin. Now in the first step, we shall write down the coordinates of the three vertices that is, vertex A has coordinates, 2, 6, vertex B has coordinates, minus 4, 2 and vertex C has coordinates, minus 4, 6. Now we know that the transformation rule for rotating a figure at 270 degrees counterclockwise is given by xy transforms to y-x. Now in the second step, we shall find image points of vertices that is A, B and C. So image point of vertex A with the coordinates 2, 6 will be given by 6 minus 2. Similarly image point of vertex B with the coordinates minus 4, 2 is given by 2 minus of minus 4 that is 4. Similarly image point of vertex C with the coordinates minus 4, 6 is given by 6 minus of minus 4 that is 4. So image point of vertex A with the coordinates 2, 6 is given by the point A prime with the coordinates 6 minus 2. Image point of vertex B with the coordinates minus 4, 2 is given by the point B prime with the coordinates 2, 4 and image point of vertex B with the coordinates minus 4, 6 is given by the point C prime with the coordinates 6, 4. Using this transformation rule, we can say that point A with the coordinates 2, 6 transforms to the point A prime with the coordinates 6 minus 2, point B with the coordinates minus 4, 2 transforms to the point B prime with the coordinates 2, 4. Similarly point C with the coordinates minus 4, 6 transforms to the point C prime with the coordinates 6, 4. Now we shall plot these points on the coordinate plane. Now we have plotted these points on the coordinate plane that is point A prime with the coordinates 6 minus 2, point B prime with the coordinates 2, 4 and point C prime with the coordinates 6, 4. 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 now we have rotated triangle ABC about origin by 270 degrees counterclockwise given by the triangle A prime B prime C prime. This is the required image of the given triangle. Here we should note that rotating a figure at 270 degrees anti-clockwise about origin is the same as rotating the figure at 90 degrees clockwise about origin. This completes our session. Hope you enjoyed this session.