Question

given directed line segment ac below, find the coordinates of b on ac such that the ratio of ab to ac is 1:3

Explanation:

Step1: Identify coordinates of A and C

From the graph, A(4,5), C(3,-1)

Step2: Calculate vector AC

AC = (3-4, -1-5) = (-1, -6)

Step3: Determine AB vector (1/3 of AC)

AB = (1/3)(-1, -6) = (-1/3, -2)

Step4: Find coordinates of B

B = A + AB = (4 - 1/3, 5 - 2) = (11/3, 3)

Answer:

(11/3, 3)