Question

Given a line segment AB with endpoints A(-12, -5) and B(9, -12), and point P dividing the line AB three-sevenths of the way from A to B, calculate the coordinates of point P.

Answer 1

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).