Question

5. Segment AB has endpoints at A(-4,-8) and B(10, 13). If point P lies on AB such that AP: BP = 2:5 then find the coordinates of P. Show all your work.​

Answer 1

To find the coordinates of P, we can use the concept of proportional division of line segments. Given that AP:BP = 2:5, it means that the ratio of the length of AP to BP is 2:5.

Let's first find the vector that represents the direction of AB, which is the vector pointing from A to B. We can find this by subtracting the coordinates of A from the coordinates of B:

(10,13) - (-4,-8) = (14, 21)

This is the vector <14,21>

Now, we can find the point P, which is located two fifths of the way from A to B, by multiplying the vector <14,21> by 2/7 and adding the result to the coordinates of A:

P = A + (2/7) * <14,21>

= (-4,-8) + (2/7) * <14,21>

= (-4,-8) + <8,6>

= (4,-2)

So, the coordinates of P are (4,-2)

We can observe that point P is two fifth of the way from A to B.