Question

show that the following sets of points are collinear and find the equation of the line L containing them are (1,3),(-2,-6),(2,6)​

Answer 1

$\underline{\textsf{Given:}}$

$\textsf{Points are (1,3), (-2,-6) and (2,6)}$

$\underline{\textsf{To find:}}$

$\textsf{The equation of  the line containing the given 3 points}$

$\underline{\textsf{Solution:}}$

$\underline{\mathsf{Formula\;used:}}$

$\mathsf{The\;equation\;of\;the\;line\;joining\;(x_1,y_1)\;and\;(x_2,y_2)\;is}$

$\boxed{\mathsf{\dfrac{y-y_1}{y_2-y_1}=\dfrac{x-x_1}{x_2-x_1}}}$

$\textsf{First we find out the equation of the line joining (1,3) and (-2,-6)}$

$\mathsf{\dfrac{y-y_1}{y_2-y_1}=\dfrac{x-x_1}{x_2-x_1}}$

$\mathsf{\dfrac{y-3}{-6-3}=\dfrac{x-1}{-2-1}}$

$\mathsf{\dfrac{y-3}{-9}=\dfrac{x-1}{-3}}$

$\mathsf{\dfrac{y-3}{3}=\dfrac{x-1}{1}}$

$\mathsf{y-3=3(x-1)}$

$\mathsf{y-3=3x-3}$

$\implies\mathsf{3x-y=0}$

$\mathsf{put\;x=2\;and\;y=6}$

$\mathsf{3(2)-6=0}$

$\mathsf{0=0}$

$\implies\textsf{(2,6)\;satsifies\;the\;equation\;3x-y=0}$

$\implies\textsf{(2,6) lies on the line 3x-y=0}$

$\therefore\textsf{The given 3 points are collinear}$

$\underline{\textsf{Answer:}}$

$\textsf{The equation of the line containing the given 3 points is 3x-y=0}$

$\underrline{\textsf{Find more:}}$

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