 Hello friends welcome to the session I am Valka. Let's discuss the given question. The two opposite vertices of a square are minus 1, 2 and 3, 2. Find the coordinates of the other two vertices. Now since we are given with a square, so let A be C be V of square as we can see from the figure D and we are given with the coordinates of A that is minus 1, 2 and C since we are given two opposite vertices. Therefore A and C are opposite vertices, so the coordinates of A are minus 1, 2 and C are 3, 2. Now we have to find the coordinates of the other two vertices that is B and D. So let the coordinates of B are x and y. Now since A, B, C, D is a square and we know that all the sides of the square are equal that is A, B equal to V, C equal to C, D equal to A, D. Now we take A, B equal to V, C or we can say A, B square equal to V, C square. Now applying distance formula to A, B and C, we get A, B square equal to x plus 1 square plus y minus 2 square that is A, B square equal to V, C square which is x minus 3 square plus y minus 2 square or this can be written as x square plus 1 plus 2x plus y square plus 4 minus 4y equal to x square plus 9 minus 6x plus y square plus 4 minus 4y. So this is equal to or we can say this can be written as 8x equal to 8 that is all simplified the above step or we can say x equal to 1. Now again from the figure we can see that A, B square plus V, C square equal to A, C square. So I am applying this we get A, B square plus V, C square equal to A, C square or this can be written as now A, B is x plus 1 square plus y minus 2 square plus V, C is x minus 3 square plus y minus 2 square equal to A, C square that is 3 plus 1 square plus 2 minus 2 square or this can be written as substituting value x equal to 1 we get 4 plus 2y minus 2 whole square plus 4 equal to 16 or we can say 2y minus 2 whole square equal to 8 or y minus 2 whole square equal to 4 or it can be written as y square plus 4 minus 4y equal to 4. So this implies y square minus 4y equal to 0, 4, 4 cancel out. So we get this implies on taking y common we get y minus 4 equal to 0. So this implies y equal to 0 and y equal to 4 the coordinates of other two vertices are 1, 0, 1, 4. Therefore the required vertices are 1, 0, 1, 4. So hope you understood the solution and enjoyed the session. Goodbye and take care.