 Hi and welcome to our session. I'm Kanika and I'm going to help you to solve the following question. The question says find the length of the meteons of the triangle with vertices a having coordinate 0 0 6, b is having coordinate 0 4 0 and c is having coordinate 6 0 0. Before solving this question we should know that if p having coordinates x 1 y 1 z 1 and q having coordinates x 2 y 2 z 2 are two points then the coordinates of the middle point of the segment p q will be x 1 plus x 2 by 2 y 1 plus y 2 by 2 z 1 plus z 2 by 2. You should also know that distance between points p and q that is p q is given by square root of x 2 minus x 1 whole square plus y 2 minus y 1 whole square plus z 2 minus z 1 whole square. The knowledge of this is the key idea in this question. Let's now begin with the solution. We are given that a b and c are three vertices of a triangle a b c. We have to find the length of the medians of this triangle. Let d be the middle point of the line segment joining points v having coordinates 0 4 0 and c having coordinates 6 0 0. Now the coordinates of t, coordinates of v will be 0 plus 6 by 2 4 plus 0 by 2 0 plus 0 by 2. This means coordinates of dr 3 2 0. Now we will find length of medial ad 0 6 and coordinates of dr 3 2 0. Now using distance formula we will find ad. Now here x 1 is equal to 0, y 1 is equal to 0, z 1 is equal to 6, x 2 is equal to 3, y 2 is equal to 2 and z 2 is equal to 0. So ad is equal to 3 minus 0 whole square plus 2 minus 0 whole square plus 0 minus 6 whole square. This is equal to square root of 9 plus 4 plus 36 and this is equal to square root of 49. And this is equal to 7 units. So distance between a and d is 7 units. Now we will find length of medial v e. Let e be the middle point of the segment joining length a having coordinates 0 0 6 and c having coordinates 6 0 0. Now we will find coordinates of e. Now coordinates of e will be 0 plus 6 by 2 0 plus 0 by 2 6 plus 0 by 2. So coordinates of e are 3 0 3. Now we will find length of medial v e, coordinates of v are 0 4 0 and coordinates of e are 3 0 3. Now using distance formula v e is equal to square root of 3 minus 0 whole square plus 0 minus 4 whole square plus 3 minus 0 whole square and this is equal to square root of 9 plus 16 plus 9. This is equal to square root of 34. So length of medial v e is square root of 34. Now let the middle point of the segment joining points a having coordinates 0 0 6 v having coordinates 0 4 0. Now coordinates of f will be 0 plus 0 by 2 0 plus 4 by 2 6 plus 0 by 2. So we have found out that coordinates of f are 0. We will find length of medial coordinates of c are 6 0 0 and coordinates of f are 0 2 3. So c f is equal to square root of 0 minus 6 whole square plus 2 minus 0 whole square plus 3 minus 0 whole square and this is equal to square root of 36 plus 4 plus 9 and this is equal to square root of 49 and this is equal to 7 units. So required lengths of the medians are 7 square root of 34 and 7. This is our required answer. So this completes the session. Bye and take care.