Question

the ratio in which the point (1,3) divides the line segment joining the points (1,7) and (4,3) is ​

Answer 1

$Let \: the \:ratio \: in \: which \: the \: P(1,3) \\divides \: the \: line \: segment \: joining \:the \\points \: A(1,7) = ( x_{1} ,y_{1}) \: and \: B(4,3) = ( x_{2} ,y_{2}) \: is \: k:1$

$\underline {\blue { By \: Section \: Formula }}$

$\Big(\frac{kx_{2}+x_{1}}{k+1} , \frac{ky_{2}+y_{1}}{k+1}\Big)= P(1,3)$

/* Take First \: Coordinates */

$\implies \frac{kx_{2}+x_{1}}{k+1} = 1$

$\implies \frac{k\times 4+1}{ k+1} = 1$

$\implies 4k + 1 = k+1$

$\implies 4k - k =1-1$

$\implies 3k = 0$

$\implies k = 0$

Therefore.,

$Point \: P \: doesn't \: divides \:the \: line$

•••♪