 Hello and welcome to the session. In this session we will discuss how to find the distance between two points on coordinate plane by using Pythagoras theorem. Now we will know how to find the horizontal length and vertical length between two points lying on same horizontal or vertical line on the coordinate plane. Now length of this horizontal line segment A v will be equal to absolute value of difference between the x coordinates which is equal to absolute value of 4 minus 2 which is equal to 2 and length of this vertical line segment P q will be equal to absolute value of difference between the y coordinates which is equal to absolute value of 4 minus 1 which is equal to but if we have any two points say D and E on the coordinate plane and we have to find distance between them when the line joining them is neither horizontal nor vertical rather it is a slanting line. Now for finding out the length of this slanting line segment we will make use of Pythagoras theorem. Now let us see how to use Pythagoras theorem. Now suppose we have a right angle triangle ABC right angle at B then here AC is called the high pattern use and also it is given AB has length P units BC with length Q units and AC with length R units. Then according to Pythagoras theorem in a right angle triangle we see square of the length of the high pattern use that is R square is equal to sum of the squares of the length of every two sides that is Q square. Now we can use this result to find distance between any two points in the coordinate plane. Now let us take two points A and B on the coordinate plane. Now coordinates of point A are minus 4 minus 2 with point B and now we will find length of this line segment AB and for this we will make use of Pythagoras theorem. First of all we will make a right angle triangle using these two points on the point B and the point where the neat right angle and coordinates of the point C are minus 1 minus 2 the length of vertical and horizontal line segments as we have discussed earlier. Now coordinates of point A are minus 4 minus 2 and coordinates of point C are minus 1 minus 2 so length of horizontal line segment AC is equal between the x square is equal to absolute value of minus 4 minus that is equal to absolute value of minus 4 plus 1 which is equal to absolute value of minus 3 that is equal to and now we can find length of vertical line segment BC which is equal to absolute value of difference between the y coordinates that is equal to absolute minus of minus is equal to absolute value of 2 plus 2 which is equal to 4. The length of hypotenuse AB by unit angle triangle is equal to plus BC square by recent lines is equal to now length of side AC is 3 units length of side BC is further be equal to and this implies AB square is equal to 3 square which is 9 plus square which is 16 and this implies AB square is equal to 25 which further gives AB is equal to square root of 25. Now taking a positive square root as length cannot be negative we get AB is equal to points A and B is thus we can find the distance between any two points on the coordinate plane. So in this session we have learnt how to apply Pythagoras theorem to points on the coordinate plane and this completes our session hope you all have enjoyed the session.