Let us assume the line divides AB in k : 1 ratio.
Coordinates of point of division can be given as follows:
x=2+3k/k+1

y=−2+7k/k+1
Substituting the values of x and y in following equation;
2x+y−4−0

Or,
 2(2+3k/k+1)+ (−2+7k/k+1)−4=0

Or, 

(4+6k/k+1)+ (−2+7k/k+1−4)=0


4+6k−2+7k−4(k+1)=0

4+6k−2+7k−4k−4=0

−2+9k=0

9k=0+2


k=2/9

Hence, the ratio is 2 : 9.
i hope it's helpful for us...

To find the ratio in which the line 2x + y - 4 = 0 divides the line segment AB, we can use the section formula.

Section Formula: The coordinates of the point P(x,y) that divides the line segment joining two points A(x₁,y₁) and B(x₂,y₂) in the ratio m:n are given by:

x = (mx₂ + nx₁) / (m + n)
y = (my₂ + ny₁) / (m + n)

Given that A(2,-2) and B(3,7), let's find the coordinates of the point where the line 2x + y - 4 = 0 intersects AB.

Step 1: Find the slope of the line 2x + y - 4 = 0
To find the slope, we can rewrite the equation in slope-intercept form:
y = -2x + 4

Comparing this with the standard form y = mx + c, we can see that the slope is -2.

Step 2: Find the equation of the line passing through A(2,-2) with slope -2
Using the point-slope form y - y₁ = m(x - x₁), we have:
y - (-2) = -2(x - 2)
y + 2 = -2x + 4
y = -2x + 2

Step 3: Find the coordinates of the point of intersection of the lines 2x + y - 4 = 0 and y = -2x + 2
To find the point of intersection, we can solve the simultaneous equations:
2x + y - 4 = 0 ...(1)
y = -2x + 2 ...(2)

Substituting equation (2) into equation (1), we have:
2x + (-2x + 2) - 4 = 0
0x - 2 = 2
-2 = 2

Since this is not a true statement, the lines are parallel and do not intersect. Therefore, the ratio in which the line 2x + y - 4 = 0 divides the line segment AB cannot be determined.

Hence, the correct answer is option 'D' (Cannot be determined).