Final answer:
The coordinates of point B that divide the segment AC in a 2:3 ratio are calculated using the section formula, resulting in the point B(4.4, 12). Given the options, none match the calculated coordinates precisely.
Step-by-step explanation:
The question is asking for the coordinates of a point B that divides the line segment AC into a particular ratio. To find the coordinates of point B, we apply the section formula which gives the coordinates of a point that divides a segment into a given ratio.
Given the points A(2, 10) and C(8, 15), and the ratio 2:3, the coordinates of point B can be found using the following equations:
For the x-coordinate:
Bx = [(m • Cx) + (n • Ax)] / (m + n)
Bx = [(2 • 8) + (3 • 2)] / (2 + 3)
Bx = [16 + 6] / 5
Bx = 22 / 5
Bx = 4.4
For the y-coordinate:
By = [(m • Cy) + (n • Ay)] / (m + n)
By = [(2 • 15) + (3 • 10)] / (2 + 3)
By = [30 + 30] / 5
By = 60 / 5
By = 12
So, point B has the coordinates B(4.4, 12). However, given the options provided, none of them exactly match the calculated point (4.4, 12). Therefore, without approximations, none of the answer choices A) (4, 12) B) (5, 13) C) (6, 14) are correct. The calculation needs to be as precise as possible in mathematics to ensure accuracy.