The endpoints of the directed line segment AB are A(−2, −3) and B(10, 6) . Find the coordinates of point P along AB so that the ratio of AP to PB is 2 to 1.

(2, 0)

Step-by-step explanation:

Using the midpoint theorem;

M(X, Y) = {ax1+bx2/a+b, ay1+by2/a+b}

Given the coordinates A(−2, −3) and B(10, 6) divided within the ratio 2 to 1;

X = ax1+bx2/a+b

X = 2(-2)+1(10)/2+1

X = -4+10/3

X = 6/3

X = 2

Similarly;

Y = ay1+by2/a+b

Y = 2(-3)+1(6)/2+1

Y = -6+6/3

Y = 0/3

Y = 0

Hence the required coordinate P is at (2, 0)