Final answer:
To find the coordinates of point P that partitions segment AB in the ratio 3:5, use the section formula. The coordinates of P are (12, 8.625).
Step-by-step explanation:
To find the coordinates of point P so that it partitions segment AB in the ratio 3:5, we can use the concept of section formula. Let's assume that point P divides the segment AB into the ratio of 3:5. The x-coordinate of P can be found using the formula:
xP = (5 * xA + 3 * xB) / (5 + 3)
Substituting the given values, we get:
xP = (5 * 2 + 3 * 16) / (5 + 3) = 12
Similarly, the y-coordinate of P can be found using the formula:
yP = (5 * yA + 3 * yB) / (5 + 3)
Substituting the given values, we get:
yP = (5 * 5 + 3 * 12) / (5 + 3) = 8.625
Therefore, the coordinates of point P are (12, 8.625).