Question

Sridhar says “points A (1, 3), B (2, 2), C (5, 1) are collinear”. Do you agree with Sridhar? Why?​

Answer 1

$\textbf{Given:}$

$\textsf{Points are A(1,3), B(2,2), and C(5,1)}$

$\textbf{To check:}$

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

$\textbf{Solution:}$

$\underline{\mathsf{Slope\;of\;AB:}}$

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

$\mathsf{=\dfrac{2-3}{2-1}}$

$\mathsf{=\dfrac{-1}{1}}$

$\mathsf{=-1}$

$\underline{\mathsf{Slope\;of\;BC:}}$

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

$\mathsf{=\dfrac{1-2}{5-2}}$

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

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

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

$\textbf{Find more:}$

Verify whether the points (-2,3), (4,2) and (10,1) are collinear or not.​

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