Question

A, B, and C are collinear. B is between A and C. If A(2, 10) and C(8, 15), what are the coordinates of B that partition the segment into a ratio of 2:3?

B:

Answer 1

The coordinates of point B that divide the segment AC in a ratio of 2:3 are approximately (4.6, 12.2).

Step-by-step explanation:

To find the coordinates of point B that partitions the segment AC into a ratio of 2:3, we can use the concept of section formula. The section formula states that if two points A(x1, y1) and C(x2, y2) are given, and a point B divides the line segment AC in the ratio m:n, then the coordinates of B can be found using the following formula:

x = (mx2 + nx1) / (m + n)

y = (my2 + ny1) / (m + n)

Substituting the given values, A(2, 10) and C(8, 15), and the ratio 2:3, we get:

x = (2*8 + 3*2) / (2 + 3) = 4.6

y = (2*15 + 3*10) / (2 + 3) = 12.2

Therefore, the coordinates of B are approximately (4.6, 12.2).