Question

Find the ratio in which p (4,m) divides the line segment joining the points A(2,3) and b (6,-3).hence find m.


Q no.10__❤___⭐_⤵

Answer 1

A(2,3) ------------------P(4,m)--------------B(6,-3)

Applying section formula ,
Let λ is the ratio by which P divides the line joining A and B.
x = (λx₂ + x₁)/(λ + 1)
here , x = 4 , x₁ = 2 , x₂ = 6
Now, 4 = (6λ + 2)/(λ + 1)
4(λ + 1) = 6λ + 2
4λ + 4 = 6λ + 2
2 = 2λ ⇒ λ = 1
Hence, p divides the line AB into 1 : 1 ratio.

Now, for y - co - ordinate
y = (λy₂ + y₁)/(λ + 1)
m = (1 × -3 + 3)/(1 + 1) = 0
Hence , m = 0

Answer 2

heya mate....*_*

Let the point P (4,m) divide the line segment joining A (2,3) and B (6,-3) in the ratio k:1.

Applying the section formula

{(mx2+nx1)/(m+n), (my2+ny1)/(m+n)},

we have (4,m) = {(6k+2)/(k+1), (-3k+3)/(k+1)}

So 4 = (6k+2)/(k+1). Solving we get k= 1.

So the ratio is 1:1. i.e., P is the mid point of AB.

Also m = (-3k+3)/(k+1) = (-3+3)/1+1 = 0. So m= 0.

hope it helps you *_*.