Point p,a,B are collinear so,area enclosed by p,a,b are =0
use formula,
1/2 (x1(y2-y3) + x2( y3 -y1) +x3 (y1- y2)=0


m=-4

Given:
- Point A: A(-2/5,6)
- Point B: B(2,8)
- Point P: P(m,3)

To find:
- The value of m

Approach:
1. Find the equation of the line passing through points A and B.
2. Use the equation of the line to find the coordinates of point P.
3. Set the y-coordinate of point P equal to 3 and solve for the x-coordinate.
4. Substitute the x-coordinate back into the equation of the line to find the value of m.

Calculations:

Step 1: Find the equation of the line passing through points A and B.

To find the equation of a line, we need the slope (m) and the y-intercept (b).

The slope (m) can be found using the formula:
m = (y2 - y1) / (x2 - x1)

Substituting the coordinates of points A and B:
m = (8 - 6) / (2 - (-2/5))
m = 2 / (2 + 2/5)
m = 2 / (2 + 10/5)
m = 2 / (2 + 2)
m = 2 / 4
m = 1/2

Now, we have the slope (m) and we can find the y-intercept (b) using the formula:
b = y - mx

Substituting the coordinates of point A and the slope:
b = 6 - (1/2)(-2/5)
b = 6 + 1/5
b = 31/5

Therefore, the equation of the line passing through points A and B is:
y = (1/2)x + 31/5

Step 2: Use the equation of the line to find the coordinates of point P.

Substituting the y-coordinate of point P (which is 3) into the equation of the line:
3 = (1/2)m + 31/5

Simplifying the equation:
(1/2)m = 3 - 31/5
(1/2)m = 15/5 - 31/5
(1/2)m = -16/5

Multiplying both sides by 2 to isolate m:
m = -16/5 * 2
m = -16/5 * 2/1
m = -32/5

Answer:
The value of m is -32/5.