Question

Determine the ratio in which the point p(m,6) divides the join of a(-4,3)and b(2,8) .also find the value of m

Answer 1

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Answer 2

Answer:

$\red {Value \:of \:m }\green {=\frac{-2}{5}}$

Step-by-step explanation:

$Let \: k:1 \:be \: required \:ratio$

$If \:the \:ratio \: in \: which \:P(m,6)\:divides \\joining \: points \: A(-4,3) = (x_{1},y_{1}) ,\:and \\B(2,8) = (x_{2},y_{2})\:is \:k:1, \: then \:the \\coordinates \:of \:the \:point \:P\:are$

$\pink { \left(\frac{kx_{2}+x_{1}}{k+1},\:\frac{ky_{2}+y_{1}}{k+1}\right)}$

$P(m,6) = \left(\frac{k\times 2+(-4)}{k+1},\:\frac{k\times 8+3}{k+1}\right)}$

$= \left(\frac{2k-4}{k+1},\:\frac{8k+3}{k+1}\right)}$

$m = \frac{2k-4}{k+1}\:---(1)$

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

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

$\implies 6k + 6 = 8k + 3$

$\implies 6 - 3 = 8k - 6k$

$\implies 3 = 2k$

$\implies k = \frac{3}{2} \:---(2)$

$Substitute \: value \: of \: k \: in \: equation \:(1),\\we \:get$

$m = \frac{2\frac{3}{2}-4}{\frac{3}{2}+1}$

$= \frac{3-4}{\frac{3+2}{2}}\\=\frac{-1}{\frac{5}{2}}\\=\frac{-2}{5}$

Therefore.,

$\red {Value \:of \:m }\green {=\frac{-2}{5}}$

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