Determine the ratio in which the line 2x + y - 4 = 0 divides the line segment joining the points A(2, -2) and B(3, 7) .

Assume the line 2x + y – 4 = 0 divides line AB joined by the two points A(2, -2) and B(3, 7) in k : 1 ratio.

Coordinates of point of division can be given as follows:

x = and y =

Substituting the values of x and y given equation, i.e. 2x + y – 4 = 0, we have

2( + (– 4 = 0

+ ( = 4

4 + 6k – 2 + 7k = 4(k+1)

-2 + 9k = 0

Or k = 2/9

Answer

Hence, the ratio is 2:9.

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