Question

The point B lies on the segment AC. Find the coordinates of B such that AB is ( 5/8) ) of AC.

A. B = (3/8)A + (5/8)C
B. B = (5/8)A + (3/8)C
C. B = (1/8)A + (7/8)C
D. B = (7/8)A + (1/8)C

Answer 1

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.