Question

find the ratio in which p(4,m) divide the line segment joining the pointsA(2,-3) and B(6,-3)hence find m

Answer 1

Answer is attached.

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brainly.in/question/3121329

Answer 2

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