 Hi and welcome to the session. I am Shashi and I am going to help you with the following question. Question says, find the area of the triangle whose vertices are minus 5, minus 1, 3, minus 5, 5, 2. First of all, let us understand that if we are given a triangle A, B, C such that coordinates of A are x1, y1, coordinates of B are x2, y2 and coordinates of C are x3, y3, then area of triangle A, B, C 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. This is the key idea to solve the given question. Now let us start with the solution. Let us assume that A, B, C is a triangle whose vertices are A, B and C. A has coordinates minus 5, minus 1. B has coordinates 3, minus 5. C has coordinates 5, 2. Now using key idea we get x1 is equal to minus 5, y1 is equal to minus 1, x2 is equal to 3, y2 is equal to minus 5, x3 is equal to 5, y3 is equal to 2. Now we can write the area of the triangle formed by the vertices A, minus 5, minus 1, B, 3, minus 5 and C, 5, 2 is given by half multiplied by x1, x1 we know is equal to minus 5, so minus 5 multiplied by y2 minus y3, y2 we can see is equal to minus 5, so minus 5 minus y3, so y3 is equal to 2, so we can write minus 5 multiplied by minus 5 minus 2 plus x2, you know x2 is equal to 3 multiplied by y3 minus y1, we know y3 is equal to 2 and y1 is equal to minus 1, so we can write 2 minus minus 1 plus x3, you know x3 is equal to 5, so 5 multiplied by y1 minus y2, we know y1 is equal to minus 1 and y2 is equal to minus 5, so we can write y1 minus y2, now simplifying further we get 1 upon 2 multiplied by minus 5 multiplied by minus 7, we know minus 5 minus 2 is equal to minus 7 plus 3 multiplied by 2 plus 1, we know minus minus sign is equal to plus sign plus 5 multiplied by minus 1 plus 5, here again minus minus becomes plus, now simplifying further we get 1 upon 2 multiplied by 35 plus 9 plus 20, now this is further equal to 64 upon 2, now we will cancel common factor 2 from numerator and denominator both and we get area of triangle is equal to 32 square units, so our final answer is area of triangle is equal to 32 square units, this completes the session, hope you understood the solution, take care and keep smiling.