 Hello and welcome to the session. Let us discuss the following question. It says, without using distance formula, show that the points minus 2, minus 1, 4, 0, 3, 3 and minus 3, 2 are the vertices of a parallelogram. Now slope of the line joining the points say x1, y1 and x2, y2 is given by y2 minus y1 upon x2 minus x1. And we also need to know that slope of parallel lines are equal. This knowledge will work as the idea. Let us now proceed on with the solution. The given points are minus 2, minus 1, b, 4, 0, 3, 3, 3 and d, minus 3, 2. Now to prove that these are vertices of a parallelogram, we need to prove that slope of parallel lines are equal. Let us we have to prove that slope of a b is equal to slope of c d and slope of b c is equal to slope of a d. Now slope of a b is given by 0 minus 1 upon 4 minus minus 2 by this formula and this is equal to 1 upon 6. Now slope of c d is given by minus 2 minus 3 upon minus 3 minus 3 and this is equal to 1 upon 6. Therefore slope of a b is equal to slope of c d. Now we need to prove that slope of b c is equal to slope of a d. Now slope of b c is given by 3 minus 0 upon 3 minus 4 and this is equal to minus 3. Now we find slope of a d. Slope of a d is given by 2 minus minus 1 upon minus 3 upon 3 minus minus 2 and this is equal to minus 3. Therefore b c is having the same slope as a d. Let us call this as 1 and this as 2. So from 1 and 2 we say that a b is parallel to c d and b c is parallel to a d. Now since opposite sides are parallel therefore we say that a b c d is a parallelogram. This completes the question. Hope you enjoy this session. Goodbye and take care.