Question

Find the value of k for which the points (-5,1) (1,k) (4,-2) are collinear

Answer 1

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

$\textsf{(-5,1), (1,k) and (4,-2) are collinear}$

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

$\textsf{The value of k}$

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

$\textsf{Let the given points be A(-5,1), B(1,k) and C(4,-2)}$

$\textsf{Since the points are collinear,}$

$\textbf{Slope of AB = Slope of AC}$

$\implies\mathsf{\dfrac{k-1}{1+5}=\dfrac{-2-1}{4+5}}$

$\implies\mathsf{\dfrac{k-1}{6}=\dfrac{-3}{9}}$

$\implies\mathsf{\dfrac{k-1}{6}=\dfrac{-1}{3}}$

$\implies\mathsf{k-1=\dfrac{-6}{3}}$

$\implies\mathsf{k-1=-2}$

$\implies\mathsf{k=-2+1}$

$\implies\boxed{\bf\,k=-1}$

$\underline{\textbf{Answer:}}$

$\textbf{The value of k is -1}$

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

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