The coordinate of l such that the ratio of KL to KM is 1 : 3 is (x/3, y/3). The correct option is therefore;
d) (x/3, y/3)
The steps with which the coordinate of l is found is as follows;
The coordinate of the point l such that the ratio of KL to KM is 1 : 3, can be found by taking the point K as the origin, and the coordinate of the point M as (x, y), therefore;
The horizontal length of the segment KL = x
The vertical length of the segment KL = y
The required ratio of the length KL to KM = 1 : 3
Therefore, the ratio of the horizontal length of the segment KL to the horizontal length of the segment KM = 1 : 3
Let a represent the horizontal length of the segment KL, we get;
a : x = 1 : 3
a/x = 1/3
a = x/3
Similarly, let b represent the horizontal length of the segment KL, we get;
b : y = 1 : 3
b/y = 1/3
b = y/3
The coordinate of the point l is therefore; (a, b) = (x/3, y/3)