 Hi and welcome to the session, let us discuss the following question, question says, find the area of the triangle whose vertices are 2, 3, minus 1, 0, 2, minus 4. First of all let us understand that if we are given a triangle ABC where coordinates of A are x1, y1, coordinates of Br, x2, y2 and coordinates of Cr, x3, y3 then area of triangle ABC is equal to half multiplied by x1 multiplied by y2 minus y3 plus x2 multiplied by y3 minus y1 plus x3 multiplied by y1 minus y2. We will use this expression as basic idea to solve the given question. Now let us start with the solution. Now we are given that vertices of the triangle are 2, 3, minus 1, 0 and 2 minus 4. Now let us assume that triangle is ABC where coordinates of A are 2, 3, coordinates of Br minus 1, 0 and coordinates of Cr 2 minus 4. Now using key idea we get x1 is equal to 2 and y1 is equal to 3. Here x2 is equal to minus 1 and y2 is equal to 0 and here x3 is equal to 2 and y3 is equal to minus 4. Now we can write area of triangle formed by vertices A, 2, 3, B minus 1, 0 and C 2 minus 4 is given by half multiplied by x1, x1 we know is equal to 2 multiplied by y2 minus y3 we know y2 is equal to 0 and y3 is equal to minus 4. So we can write 0 minus minus 4 plus x2 we know x2 is equal to minus 1 so we can write minus 1 multiplied by y3 minus y1, y3 is equal to minus 4 minus y1, y1 is equal to 3. Now next term is x3 multiplied by y1 minus y2 we know x3 is equal to 2 and y1 is equal to 3 and y2 is equal to 0. So we can write 3 minus 0 here now this is equal to half multiplied by 2 multiplied by 0 plus 4 we know negative negative signs form positive sign plus minus 1 multiplied by we know minus 4 minus 3 is equal to minus 7. So we can write minus 1 multiplied by minus 7 plus 2 multiplied by 3 minus 0 is 3 so we can write 2 multiplied by 3. Now simplifying it further we get half multiplied by 8 plus 7 plus 6 now simplifying it further we get 21 upon 2 square units so the area of the triangle is 21 upon 2 square units this is our required answer this completes the session hope you understood the session take care and have a nice day.