Question

find the equation of the straight line passing through the origin and dividing the segment of the straight line joining (4,-2) and (1,10) internally in the ratio 2:1 ​

Answer 1

Answer:

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Step-by-step explanation:

$to \: find : \\ equation \: of \: straight \: line \\ \\ so \: here \\ as \: the \: straight \: line \: passes \: through \: \\ origin \\ let \: then \\ (x1,y1) = (0,0)$

$moreover \: this \: line \: divides \: certain \\ segment \: in \: ratio \: 2 : 1 \\ so \: let \: it \: divide \: in \: ratio \\ m : n = 2 : 1 \\ \\ moreover \: let \: here \\ (a1,b1) = (4, - 2) \\ \\ (a2,b2) = (1,10) \\ \\ so \: by \: \: applying \: \\ section \: formula \\ we \: get \\ \\ x = \frac{ma2 + na1}{m + n} \: \: ,y = \frac{mb2 + nb1}{m + n} \\ \\ = \frac{(2 \times 1) + (1 \times 4)}{2 + 1} \: \: , \: = \frac{(2 \times 10) + (1 \times ( - 2))}{1 + 2} \\ \\ = \frac{2 + 4}{3} \: \: , \: = \frac{20 - 2}{3} \\ \\ = \frac{6}{3} \: , \: = \frac{18}{3} \\ \\ = (x,y) = (2,6) \\ \\ let \: then \\ \\ (x2,y2) = (2,6)$

$so \: we \: know \: that \\ two - points \: equation \: of \: \\ straight \: line \: is \: given \: by \\ \\ \frac{y - y1}{y1 - y2} = \frac{x - x1}{x1 - x2} \\ \\ \frac{y - 0}{0 - 6} = \frac{x - 0}{0 - 2} \\ \\ = \frac{y}{ - 6} = \frac{x}{ - 2} \\ \\ - 2y = - 6x \\ \\ 6x - 2y = 0 \\ \\ 2(3x - y) = 0 \\ \\ 3x - y = 0 \\ \\ or \\ \\ y = 3x$

$hence \: required \: equation \: of \\ straight \: line \: is \: \\ 3x - y = 0$