Final answer:
To find the coordinates of point S, we need to divide the line segment QR into two parts in a ratio of 2:5. The coordinates of point S are (3, 5).
Step-by-step explanation:
To find the coordinates of point S, we need to divide the line segment QR into two parts in a ratio of 2:5. Here's how we can do it:
1. Find the difference in x-coordinates between Q and R: 8 - 1 = 7
2. Find the difference in y-coordinates between Q and R: 10 - 3 = 7
3. Multiply the x-coordinate difference by 2/7 to get the x-coordinate of S: 1 + (7 * 2/7) = 3
4. Multiply the y-coordinate difference by 2/7 to get the y-coordinate of S: 3 + (7 * 2/7) = 5
The student is asking to find the coordinates of point S that divides the line segment QR with endpoints Q(1,3) and R(8,10) into two parts with lengths in the ratio of 2:5. To find the coordinates of S, we must use the section formula in coordinate geometry.
The section formula gives the coordinates of a point which divides a line segment into two parts with a given ratio. For two points Q(x1, y1) and R(x2, y2), the point dividing the segment in the ratio m:n has coordinates ((mx2 + nx1) / (m + n), (my2 + ny1) / (m + n)). Given the ratio 2:5, we apply the formula as follows:
Coordinates of S = ((5*1 + 2*8) / (2 + 5), (5*3 + 2*10) / (2 + 5)) = ((5 + 16) / 7, (15 + 20) / 7) = (21 / 7, 35 / 7) = (3, 5).
Thus, the coordinates of point S are (3, 5).