 Hello and welcome to the session. In this session we are going to discuss the following question which says that find the distance between the points A with the coordinates minus 4 3 and B with the coordinates 2 minus 3 on our line L. Also find the midpoint of the line segment AB. We know that distance between any two points say A and B with the coordinates x1, y1 and x2, y2 respectively is given by the formula square root of x2 minus x1 the whole square plus y2 minus y1 the whole square. That is if we are given any line L and if A and B are two points on the line where A has coordinates x1, y1 and B has coordinates x2, y2 then distance between points A and B will be given by square root of x2 minus x1 the whole square plus y2 minus y1 the whole square or we can say that distance between any two points is given by this formula. Now suppose if C is the midpoint of the line segment AB then coordinates of C will be given by x1 plus x2 the whole upon 2 y1 plus y2 the whole upon 2 with this key idea we shall proceed to the solution in the question we are given two points A and B with the coordinates minus 4 3 and 2 minus 3 respectively and we need to find the distance between these two points. Now let us draw these two points on the coordinate plane that is point A with the coordinates minus 4 3 that is we have taken minus 4 on x axis and 3 on y axis and we get this point as A with the coordinates minus 4 3 and now we plot point B with the coordinates 2 minus 3 and here we take 2 on x axis and minus 3 on y axis and we get this point as B with the coordinates 2 minus 3. Now we will join these two points and then we extend AB on both sides and we get a line L and now we have to find the distance between these two points or we can say we have to find the length of the line segment AB and from our key idea we know that distance between any two points say A and B with the coordinates x1 y1 and x2 y2 respectively is given by square root of x2 minus x1 b whole square plus y2 minus y1 b whole square and here we are given that point A have coordinates minus 4 3 and point B have coordinates 2 minus 3. Now we shall find the distance AB by using distance formula that is square root of x2 minus x1 b whole square that is 2 minus of minus 4 b whole square plus y2 minus y1 b whole square that is minus 3 minus 3 b whole square which implies that AB is equal to square root of 2 minus of minus 4 which can be written as 2 plus 4 b whole square plus minus 3 minus 3 which is equal to minus 6 b whole square that is AB is equal to square root of 2 plus 4 b whole square that is 6 square which is equal to 36 plus minus 6 b whole square is equal to 36 therefore AB is equal to square root of 36 that is 72 which can be written as square root of 6 into 6 into 2 that is equal to 6 into square root of 2 units so we say that the distance AB is equal to 6 into square root of 2 units and now next part of the question says also find the midpoint of the line segment AB that is we have to find the midpoint of the line segment AB let c be the midpoint of line segment AB that is let c be the midpoint of the line segment AB and now we have to find coordinates of point C and from the key idea we know that if we are given any line segment AB their point A has coordinates x1, y1 and point B has coordinates x2, y2 and we have to find the coordinates of the midpoint of the line segment AB let's say c is the midpoint of the line segment AB then coordinates of point C are given by x1 plus x2 the whole upon 2 y1 plus y2 the whole upon 2 now here also if we assume the coordinates of point A as x1, y1 and coordinates of point B as x2, y2 then the coordinates of the midpoint C are given by x1 plus x2 the whole upon 2 y1 plus y2 the whole upon 2 which is equal to x1 plus x2 the whole upon 2 that is minus 4 plus 2 the whole upon 2 y1 plus y2 the whole upon 2 that is 3 plus of minus 3 the whole upon 2 and the equal to minus 4 plus 2 that is minus 2 upon 2 3 plus of minus 3 that is 3 minus 3 which is equal to 0 upon 2 that is minus 2 upon 2 is equal to minus 1 and 0 by 2 can be written as 0 so we say that the coordinates of the midpoint C are given by minus 1 0 but we say that the distance AB is equal to 6 into square root of 2 units and the coordinates of the midpoint of the line segment AB are given by minus 1 0 this completes our session hope you enjoyed this session