The coordinates of point B on segment AC such that the ratio of AB to BC is 2 : 3 is (12 / 5, 38 / 5).
In this problem we must use the concept of segment ratios and linear algebra operations to determine the location of a point within a line segment generated by two distinct points:
B(x, y) = A(x, y) + (AB / AC) · [C(x, y) - A(x, y)]
B(x, y) = (0, 4) + (2 / 5) · [(6, 13) - (0, 4)]
B(x, y) = (0, 4) + (2 / 5) · (6, 9)
B(x, y) = (0, 4) + (12 / 5, 18 / 5)
B(x, y) = (12 / 5, 38 / 5)
The coordinates of point B on segment AC such that the ratio of AB to BC is 2 : 3 is (12 / 5, 38 / 5).
The statement is incomplete, complete form is shown below:
Given that A (x, y) = (0, 4) and C (x, y) = (6, 13). What are the coordinates of point B on AC such that the ratio of AB to BC is 2 : 3.
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