 Hello and how are you all today? The question says if a-3, 2, b, p, q and c, having coordinates minus 1, 4, our vertices of an isosceles triangle such that a, b is equal to b, c, need to show that p plus q is equal to 1. So let us proceed with the solution. Let us draw a rough diagram to model the situation. Here we have an isosceles triangle, a, b, c where a, b is equal to b, c. The coordinates of a are minus 3, 2 respectively, b are p, q and c are minus 1, 4. Right? We need to show that p plus q is equal to 1. Now we are given over here that a, b is equal to b, c. So if a, b is equal to b, c, then a, b square is also equal to b, c square. Right? Now let us find out or write down the distance of a, b. That is minus 3 minus p the whole square plus 2 minus q the whole square. Here it will be p plus 1 the whole square plus q minus 4 the whole square. Right? Now there is square root will get cancelled out with the square and we have to solve it also. So it will be 9 plus p plus p square minus sorry plus 6p plus 4 plus q square minus 4q is equal to p square plus 2p plus 1 plus q square plus 16 minus 8q. Now on simplifying we have p minus 2p minus 4q plus 8q equal to 17 minus 13 which further implies 4p plus 4q is equal to 4. Now on dividing both the sides where 4 we have p plus q equal to 1 which was needed to be proved in this question. Right? So this completes the session. Hope you understood it. Have a nice day.