Final answer:
To find the coordinates of point B such that AB is (5/8) of AC, we apply the section formula with the appropriate weights to A and C. The correct representation for the coordinates of B is B = (3/8)A + (5/8)C.
Step-by-step explanation:
The objective is to find the coordinates of point B such that AB is (5/8) of AC. To achieve this, we need to divide the segment AC into parts in ratio 5:8, with AB being 5 parts of the total 8 parts.
We can use the concept of the section formula to determine the coordinates of B. The weight applied to A should be proportional to the length of BC, and the weight applied to C should be proportional to the length of AB. So, if AB is (5/8) of AC, then BC is (3/8) of AC because the whole segment AC has to add up to 1, or 8/8.
Therefore, the coordinates of B can be calculated using the ratio of distances from A to C, which means the coordinates of B are given by the linear combination (3/8)A + (5/8)C. So the correct answer is:
B = (3/8)A + (5/8)C.