 Hello friends, welcome to the session. I am Malka. Let's discuss the given question. The class 10 student of a secondary school in Krishnagar have been allotted a rectangular plot of land for their gardening activity. Sapling of Gulmohar are planted on the boundary at a distance of 1 meter from each other. There is a triangular grassy lawn in the plot as shown in the figure 7.14. The students are to sow seeds of flowering plants on the remaining area of the plot. In our first part, taking A as a region, find the coordinates of the vertices of the triangle. Second part, what will be the coordinates of the vertices of triangle PQR if C is the origin. Also calculate the area of triangles in these cases. What do you observe? Here is the figure A, B, C, D as a rectangular plot of land with PQR as a triangular grassy lawn. Now according to our question, we have to take A as the origin and find the coordinates of the vertices of the triangle that is P, Q and R. Now let's begin with the solution. Taking origin, taking A, B, A, D coordinate X's. So coordinate of P, take A as the origin then coordinates of P, R, 4 and 6. Coordinate of Q, R, 3 and 2. Coordinate of, so hope you understood it. Now let's see the next part. In the second part, we have to find the coordinates of the vertices of P, Q, R by taking C as origin. If we take C as origin, let me count from here. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 and 15. Now we have to find the coordinates of P, Q and R. Taking, taking C, V, C, D, we'll find the coordinate of P, Q and R. Then coordinates, it is 12, coordinates of Q are 13. Coordinates, we understood how to find the coordinates of P, Q, R by taking C as origin. Now we have to also calculate the areas of the triangles in these cases. That is where A is the origin and the second case where C is the origin. And we have to also tell what does V observe. Now we know that area with vertices A with coordinates x1, y1, V, x2, y2 and C with coordinates x3, y3 is 1 upon 2 into x1, y2, minus y3 plus x2, y3 minus y2 plus x3, y1 minus y2. Using this formula we'll find the area of the triangle whose vertices are P, Q and R and where A is the origin. And taking A, D and A, B as coordinate x's. Now we already know the coordinates of point P, Q and R where A is the origin and the coordinates of point P are 4, 6, Q, R, 3, 2 and R where origin. Now we find the area of the triangle that is area of triangle P, Q, R equal to 1 upon 2, x1 will be 4, 2 minus 5 plus 3, 5 minus 6 plus 6 into 6 minus 2. 1 by 2 into minus 12 minus 3 plus 24. This is equal to 9 by 2 square units. Now we find the area of the triangle P, Q, R where C is the origin and C, B and C, D are coordinate x's. And we know the coordinates of P, Q, R, coordinates P, coordinates of Q, R, 13, 6 and coordinates of R, 10, 3. Now we find the area of the triangle P, Q, R where C is the origin. So area of triangle P, Q, R is equal to 1 by 2 into 12 into 6 minus 3 plus 13 into 3 minus 2 plus 10 into 2 minus 6. So this is equal to 1 by 2 into 36 plus 13 minus 14. This is equal to 9 by 2 square units. Here we observe that the area of both the triangles with where A was the origin and where C is the origin is same. Thus we see that the coordinates of the point P, Q, R where A is the origin are 4, 6, 3, 2, 6, 5 taking A, B and A, B as coordinate x's. And the coordinates of the point P, Q, R with 3 as origin are 12, 2, 13, 6, 10, 3 taking C, B and C, B as coordinate x's. And area of both the triangles where A was the origin and where C was the origin is 9 by 2 square units. We see that area of both the triangles is same. So hope you understood the solution and enjoyed the session. Goodbye and take care.