Final answer:
The coordinates of the point that divide the line segment (0, 0) and (2, 3) in the ratio 2:1 are (4/3, 2).
Step-by-step explanation:
To find the coordinates of the point that divides the line segment joining the points (0, 0) and (2, 3) in the ratio 2:1, we can use the concept of section formula. The section formula states that the coordinates of the point that divides a line segment joining two points A(x1, y1) and B(x2, y2) in the ratio m:n are given by:
[(mx2 + nx1)/(m + n), (my2 + ny1)/(m + n)]
Applying this formula, substitute the values: (x1, y1) = (0, 0), (x2, y2) = (2, 3), m = 2, and n = 1.
[(2 * 2 + 1 * 0)/(2 + 1), (2 * 3 + 1 * 0)/(2 + 1)]
Simplifying the expression, we get:
(4/3, 6/3)
The coordinates of the point that divides the line segment in the ratio 2:1 are (4/3, 2).
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