Question

If the point P(m,3) lies on the line segment joining the points A(-2/5,6) and B(2,8) then find the value of m ( By section formula )

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Answer 1

Answer:

Step-by-step explanation:

let the ratio in which they are divided be k:1

then by section formula ,

(m,3) = {k*2+1*-2/5 /k+1, k*8+1*6 /k+1}

3=8k+6/k+1

3k+3=8k+6

5k= -3

then k= -3/5  

m=2*-3/5+ (-2/5) /-3/5+1

m=-8/5 /-3/5+1

m=-8/2

m= -4

Answer 2

The value of m is -4.

Step-by-step explanation:

It is given that point P(m,3) lies on the line segment joining the points A(-2/5,6) and B(2,8).

Let point P divides the line AB in k:1.

Section formula: If a point divides a line segment in m:n, then the coordinates of that point are

$(\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n})$

Using section formula, the coordinates of point P are

$P(m,3)=(\frac{(k)(2)+(1)(-\frac{2}{5})}{k+1},\frac{(k)(8)+(1)(6)}{k+1})$

$P(m,3)=(\frac{2k-\frac{2}{5}}{k+1},\frac{8k+6}{k+1})$        ... (1)

On comparing both sides we get

$m=\frac{2k-\frac{2}{5}}{k+1}$        ... (1)

$\frac{8k+6}{k+1}=3$

$8k+6=3(k+1)$

$8k+6=3k+3$

$8k-3k=-6+3$

$5k=-3$

$k=-\frac{3}{5}$

The value of k is -3/5. Substitute this value in equation (1).

$m=\frac{2(\frac{-3}{5})-\frac{2}{5}}{(\frac{-3}{5})+1}$

$m=\frac{\frac{-6}{5})-\frac{2}{5}}{\frac{-3+5}{5}}$

$m=\frac{\frac{-8}{5}}{\frac{2}{5}}$

$m=\frac{-8}{2}$

$m=-4$

Therefore the value of m is -4.

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