Final answer:
The problem is solved using the section formula to find the coordinates of the point that divides the segment between D (-7, 5) and T (7, -9) in a 4 to 3 ratio using weighted averages of the given points' coordinates.
Step-by-step explanation:
The question involves finding a point that divides the segment between points D (-7, 5) and T (7, -9) in a specific ratio, which falls under the branch of coordinate geometry, a part of Mathematics. To find the point that partitions the segment in a 4 to 3 ratio, we use the section formula. The formula involves the weighted average of the x-coordinates and the y-coordinates separately, considering the given ratio.
To calculate the point P(x, y) that divides the segment DT in a 4:3 ratio, the coordinates of point P are determined as follows:
- x-coordinate, x = [(4 * Tx) + (3 * Dx)] / (4 + 3)
- y-coordinate, y = [(4 * Ty) + (3 * Dy)] / (4 + 3)
Substituting the given coordinates D (-7, 5) and T (7, -9), we get:
- x = [(4 * 7) + (3 * -7)] / 7
- y = [(4 * -9) + (3 * 5)] / 7
After calculating the values, we can establish the exact coordinates of the point that divides the segment in the required ratio.