Question

Let AB be the directed line segment beginning at point A(2 , 4) and ending at point B(17 , 17). 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. B. C. D.

Answer 1

Answer: Thus, the answer is (14.5, 14.83).

Step-by-step explanation:  Given that A(2, 4) and B(17, 17) are the end points of a directed line segment AB . We are find the point P on the line segment AB which divides it in the ratio AP : PB = 5 : 1. See the attached figure.

The co-ordinates of point P will be

$P\\\\\\=\left(\dfrac{5\times 17+1\times 2}{5+1},\dfrac{5 \times 17+1\times 4}{5+1}\right)\\\\\\=\left(\dfrac{87}{6},\dfrac{89}{6}\right)\\\\\\=(14.5,14.83).$

Therefore, the co-ordinates of point P are (14.5, 4.83).

Thus, the answer is (14.5, 14.83).