Question

find the ratio in which the point P(x,2) divides the line segment joining points A(12,5) and B(4,-3). Also find value of x

Answer 1

Since P divides the line segment joining points A(12,5) and B(4,-3) therefore,
$x= \frac{m x_{2}+n x_{1} }{m+n}$ and
$y= \frac{m y_{2}+n y_{1} }{m+n}$
where m:n is the ratio;
(x₁,y₁)=(12,5) and (x₂,y₂)=(4,-3) and (x,y)=(x,2) (coordinate of P)
∴, $2= \frac{-3m+5n}{m+n}$
or, $2m+2n=-3m+5n$
or, $2m+3m=5n-2n$
or, $5m=3n$
or, $\frac{m}{n}= \frac{3}{5}$
∴, $x= \frac{3.4+5.12}{3+5}$
or, $x= \frac{12+60}{8}$
or, $x=72/8$
or, $x=9$
∴, The required ratio is $\frac{3}{5}$ and $x=9$. Ans.

Answer 2

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