Question

What are the coordinates of point B on AC such that the ratio of AB to BC is 2:3

Answer 1

the answer is c, it fits the ratio given and is 2:3

Answer 2

The coordinates of point B on AC such that the ratio of AB to BC is 2:3 are: A.
`(2 (1)/(5), (1)/(5))`.

In this scenario, line ratio would be used to determine the coordinates of the point B on the directed line segment AB that partitions the segment into a ratio of 2 to 3.

In Mathematics and EuclideanGeometry, line ratio can be used to determine the coordinates of a point and this is modeled by this mathematical equation:

`M(x, y) = (((mx_2 + nx_1))/((m + n)), (((my_2 + ny_1))/((m + n)))`

By substituting the given points (-1, -1) and (7, 2) into the formula for line ratio, we have;

`B(x, y) = (((mx_2 + nx_1))/((m + n)), (((my_2 + ny_1))/((m + n)))\\\\B(x, y) = (((2(7) + 3(-1)))/((2 + 3)), (((2(2) + 3(-1)))/((2 + 3)))\\\\B(x, y) = (((14 -3))/((5)), (((4 -3))/((5)))\\\\B(x, y) = (((11))/((5)), (((1))/((5)))\\\\B(x, y) = (2 (1)/(5), (1)/(5))`