Final answer:
To locate point P on the segment AB which is divided in the ratio 3:7, calculate the partial differences in x and y, multiply by 3/7 and add these changes to A's coordinates. Point P is found to be at (-3, -8).
Step-by-step explanation:
To find the coordinates of point P that divides the line segment AB three-sevenths of the way from A to B, we first need to find the difference in the x and y coordinates of A(-12, -5) and B(9, -12), and then multiply these by 3/7 to find the part of the segment that point P will divide.
The change in x is: (9 - (-12)) = 21. The change in y is: (-12 - (-5)) = -7.
Multiplying these by 3/7 gives the change from A to P:
- x change: 21 * 3/7 = 9
- y change: -7 * 3/7 = -3
Now we add these changes to the coordinates of A:
- x coordinate of P: -12 + 9 = -3
- y coordinate of P: -5 - 3 = -8
So, the coordinates of point P are (-3, -8).