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Given:
Line segment AB has one endpoint at A(0,0).
(5, 3) is 1/3 of the way from A to B.
To find:
The coordinates of point B.
Solution:
Let the coordinates of point B are (a,b).
Suppose point P(5, 3) is 1/3 of the way from A to B.
It means, point P(5, 3) divides the segment AB in 1:2.
Section formula:
If a point divides a line segment in m:n, then
Point P(5, 3) divides the segment AB in 1:2. Using section formula, we get
On comparing both sides, we get
Therefore, the coordinates of point B are (15,9).