 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that find the distance between the coordinates 2-2 and 4-5 using Pythagorean theorem. We know that Pythagorean theorem states in a right angle triangle, sum of squares of length of legs is equal to square of length of hypotenuse that is in a right angle triangle ABC if C represents the length of the hypotenuse and if A and B are the length of the legs of the triangle then we have A squared plus B squared is equal to C squared. With this key idea let us proceed to the solution. Now let us suppose A be the point with the coordinates 2-2 and B be the point with the coordinates 4-5. Now we should plot these points on the coordinate plane. We have point A with the coordinates 2-2 so we label this point as A and point B has coordinates 4-5 so we label this point as B. Now we join the two points to get a straight line AB. Now we draw a horizontal line from A and a vertical line from B and see where we both meet on the coordinate plane. We put a dot here and label this point as C. Now we can see point C has coordinates 4-2 so we get a right angle triangle ABC. Now let length of AC be A, BC be B and AB be C that is let length of AC be A, BC be B and AB be C. Now we shall find lengths A, B and C. Now we see that the distance between A and C is 2 units so length of AC that is A is equal to 2 units the distance between B and C is 7 units so we say length of BC that is B is equal to 7 units. Now we have got the length of AC and BC and here we need to find the distance between two points A and B for this we shall find length of the side AB and from the key idea we know that Pythagorean theorem states that in a right angle triangle sum of squares of length of legs is equal to square of the length of hypotenuse and A square plus B square is equal to C square so here in triangle ABC we see that AB is the hypotenuse and AC and CB are the two legs of the right angle triangle therefore applying Pythagorean theorem we get C square is equal to A square plus B square here C is the hypotenuse and A and B are the two legs of the triangle and therefore we get C square is equal to A square that is 2 square plus B square that is 7 square so we get C square is equal to 2 square that is 4 plus 7 square 49 that is C square is equal to 53 or we can say that C is equal to square root of 53 now taking the positive square root of 53 we get the value of C as 7.3 approximately so we can say that the distance between the points is 7.3 units which is the required answer this complete file session hope you enjoyed this session