The ratio of the segments after the partition is 5:3.
5 + 3 = 8
A point that partitions a segment in a ratio of 5:3 is 5/8 of the way from the beginning. You need to find the difference between the x-coordinates of points A and C, multiply by 5/8, and add to the x-coordinate of point A to find the x-coordinate of point B. Then do the same for the y-coordinates.
Difference in x-coordinates from A to C:
11 - (-5) = 11 + 5 = 16
5/8 of the difference = 5/8 * 16 = 10
Add 10 to -5: -5 + 10 = 5
The x-coordinate of B is 5
Difference in y-coordinates from A to C:
0 - 2 = -2
5/8 of the difference = 5/8 * (-2) = -5/4 = -1.25
Add -1.25 to 2: -1.25 + 2 = 2 - 1.25 = 0.75 = 3/4
The y-coordinate of B is 3/4
Answer: B. (5, 3/4)