Question

determine the whether of points are collinear (3) R(0,3) , D(2,1) , S(3,-1)​

Answer 1

Answer:

$R (0,3) = (x_{1} , y_{1} )$

$D (2,1) = ( x_{2} , y_{2}$

$S ( 3 , -1) = ( x_{3} , y_{3} )$

$\displaystyle \: Slope \: of \: line \: RD = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

$\displaystyle \: = \frac{1-3}{2-0}$

$\displaystyle = \frac{-2}{2}$

$\displaystyle \therefore \: Slope \: of \: line \: RD = -1$

$\displaystyle \: Slope \: of \: line \: DS = \frac{-1-1}{3-2}$

$\displaystyle \: = \frac{-2}{1}$

$\therefore \: Slope \: of \: line \: DS = -2$

$Slope \: of \: line \: RD \neq \: Slope \: line \: DS$

$\therefore \: Points \: R, \: D \: and \: S \: are \: not \: collinear$