Question

Points A(3,1) B(12,-2) C(0,2) cannot be the vertices of a triangle

Answer 1

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

$\textsf{A(3,1), B(12,-2) and C(0,2)}$

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

$\textsf{A,B and C cannot be vertices of a triangle}$

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

$\begin{array}{rl}\mathsf{Slope\;of\;AB}&\mathsf{=\dfrac{y_2-y_1}{x_2-x_1}}\\\\&\mathsf{=\dfrac{-2-1}{12-3}}\\\\&\mathsf{=\dfrac{-3}{9}}\\\\&\mathsf{=\dfrac{-1}{3}}\end{array}$

$\begin{array}{rl}\mathsf{Slope\;of\;BC}&\mathsf{=\dfrac{y_2-y_1}{x_2-x_1}}\\\\&\mathsf{=\dfrac{2+2}{0-12}}\\\\&\mathsf{=\dfrac{4}{-12}}\\\\&\mathsf{=\dfrac{-1}{3}}\end{array}$

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

$\implies\textsf{The points A,B and C are collinear}$

$\textbf{Hence they cannot be vertices of any triangle}$

$\underline{\textbf{Formula used:}}$

$\boxed{\begin{minipage}{7cm} \\\mathsf{Slope\;of\;line\;joining\;the\;points\;(x_1,y_1)\;and}\\\\\mathsf{(x_2,y_2)\;is\;\;\;m=\dfrac{y_2-y_1}{x_2-x_1}}\\ \end{minipage}}$

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