Question

1)Let AB be the directed line segment beginning at point A(1 , 1) and ending at point B(-4 , 6). Find the point P on the line segment that partitions the line segment into the segments AP and PB at a ratio of 5:1.
A)(-3 1/6,5 1/6)
B)(1/6,1 5/6) <----
C)(-3 4/5,31)
D)(-2 1/6, 6 1/6)

I think it's B but I'm not completely sure.

Answer 1

B) divides AB in the ratio 1:5, but not 5:1.

look for a choice which is 5/6 from point B instead.

Answer 2

A(1, 1). P(x, y), B(-4, 6).
5u + u = 1. u = 1/6, 5u = 5/6.
x-1 = 5/6(-4-1)
x = -19/6 = -3 1/6.

y-1 = 5/6(6-1)
y = 31/6 = 5 1/6.

Answer 3

Let AB be the directed line segment beginning at point A(5 , 1) and ending at point B(11 , 16). Find the point P on the line segment that partitions the line segment into the segments AP and PB at a ratio of 4:5.