Find the coordinates of point B that lies along the directed line segment from A(-5, 2) to C(11, 0) and partitions the segment in the ratio of 5:3.

Question

1. A. (10, 5)
2.  B. (6, 2)
3.  C. (3, 1)
4.  D. (5,3/4)

Answer 1

Since we are dividing the segment in the ratio 5:3, the segment is being divided into 8 (5+3) equal parts.

We are looking for the point B on AC that lies 5/8 of the way from A to C.

As we move along AC from A to C, x increases by 16 and y decreases by 2.

x-coordinate of B is: -5 + (5/8)(16) = -5 + 10 = 5

y-coordinate of B is: 2 - (5/8)(2) = 2 - 1.25 = 0.75

So, B = (5, 0.75)