Final answer:
To find the coordinates of point F=(x, y), we can use the formula for partitioning a line segment. Substituting the given values into the formulas, we find that the coordinates of point F are (7, 3).
Step-by-step explanation:
To find the coordinates of point F, we need to use the concept of partitioning in a given ratio. Let's say the coordinates of point F are (x, y). The given ratio is 2:5, which means that the distance from point E to P is two parts and the distance from P to F is five parts.
Using the formula for partitioning a line segment, we can find the coordinates of point F:
x-coordinate of F = (5 * x-coordinate of P + 2 * x-coordinate of E) / (5 + 2)
y-coordinate of F = (5 * y-coordinate of P + 2 * y-coordinate of E) / (5 + 2)
Substituting the values of point P (1, 2) and point E (9, 6) into the formulas, we get:
x-coordinate of F = (5 * 1 + 2 * 9) / 7 = 7
y-coordinate of F = (5 * 2 + 2 * 6) / 7 = 3
Therefore, the coordinates of point F are (7, 3).