 Hi, and welcome to our session. Let us just ask the following question. The question says a point r with x-coordinate 4 lies on the line segment joining the points p having coordinates 2 minus 3, 4, and q having coordinates 8, 0, 10, pying the coordinates of r. Let's now begin with the solution. We are given that a point r with x-coordinate 4 lies on the line segment joining the points p having coordinates 2 minus 3, 4, and q having coordinates 8, 0, 10. And we have to find the coordinates of r. Let the coordinates coordinate 4 y-segment having coordinates 2 minus 3, 4 having coordinates 8, 0, 10. Therefore, 4 y-segment divides the line segment into the points having coordinates 2 minus 3, 4, and q having coordinates 8, 0, 10 in the ratio is 2, 1. By the section formula, we know that it coordinates x1, y1, z1, and q having coordinates x2, y2, z2 are two points. Then the coordinates of the point that divides the line segment pq internally in the ratio m is to nr, mx2 plus nx1 upon m plus n, my 2 plus n by 1 upon m plus n, mz2 plus nz1 upon m plus n. So by section formula, coordinates of r will be 8k plus 2 by k plus 1, 0k minus 3 by k plus 1, 10k plus 4 by k plus 1. The coordinates of the r on k plus 1 equals to 4. This implies 8k plus 2 is equal to 4k plus 4. This implies 4k is equal to 2. And this implies k is equal to 1 by 2. Now we will substitute value of k in y and z coordinate. Now y coordinate is equal to 0k minus 3 upon k plus 1. By substituting value of k, we get minus 3 by 1 plus 2 by 1 by 2 plus 1. This is equal to minus 3 by 3 by 2. And this is equal to minus 6 by 3. And this is equal to minus 2. Now z coordinate is equal to 10k plus 4 by k plus 1. Substitute the value of k. By substituting value of k, we get 10 into 1 by 2 plus 4 upon 1 by 2 plus 1. This is equal to 5 plus 4 by 3 by 2. This is equal to 18 by 3. And this is equal to 6. So z coordinate of r is 6. Hence the coordinates minus 2, this is our required answer. So this completes the session. Bye and take care.