Question

determine if points 6,8 2,3 and -2 ,-11 are collinear​

Answer 1

$\underline{\textbf{Given:}}$

$\textsf{Points are (6,8), (2,3) and (-2,-11)}$

$\underline{\textbf{To check:}}$

$\textsf{whether the given points are collinear or not}$

$\underline{\textbf{Solution:}}$

$\textsf{Let the given points be A(6,8), B(2,3) and C(-2,-11)}$

$\textsf{Slope of AB}$

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

$\mathsf{=\dfrac{3-8}{2-6}}$

$\mathsf{=\dfrac{-5}{-4}}$

$\mathsf{=\dfrac{5}{4}}$

$\textsf{Slope of BC}$

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

$\mathsf{=\dfrac{-11-3}{-2-2}}$

$\mathsf{=\dfrac{-14}{-4}}$

$\mathsf{=\dfrac{7}{2}}$

$\implies\mathsf{Slope\;of\;AB{\neq}Slope\;of\;BC}$

$\therefore\textsf{The given points are not collinear}$