Question

13).
Verify whether the points (-2,3), (4,2) and (10,1) are collinear or not.​

Answer 1

$\textbf{Given:}$

$\textsf{Points are (-2,3), (4,2), and (10,1)}$

$\textbf{To check:}$

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

$\textbf{Solution:}$

$\textsf{Let the given points be A(-2,3), B(4,2), and C(10,1)}$

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

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

$\mathsf{=\dfrac{2-3}{4+2}}$

$\mathsf{=\dfrac{-1}{6}}$

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

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

$\mathsf{=\dfrac{1-2}{10-2}}$

$\mathsf{=\dfrac{-1}{8}}$

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

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

$\textbf{Find more:}$

Verify whether the points (3,-2,4),(1,0,-2)and (-1,2,-8) are collinear

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Answer 2

SOLUTION

TO CHECK

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

CONCEPT TO BE IMPLEMENTED

Three given points are said to be collinear if the area of the triangle formed by the given points is zero

EVALUATION

Here the given points are (-2,3),(4,2) and (10,1)

Now area of the triangle formed by the given three points

$\displaystyle \sf{ = \frac{1}{2} \bigg| - 2(2 - 1) + 4(1 - 3) + 10(3 - 2)\bigg| \: \: sq.unit }$

$\displaystyle \sf{ = \frac{1}{2} \bigg| - 2 - 8 + 10\bigg| \: \: sq.unit }$

$\displaystyle \sf{ = \frac{1}{2} \times 0\: \: sq.unit }$

$\displaystyle \sf{ = 0\: \: sq.unit }$

FINAL ANSWER

Hence the points (-2,3),(4,2) and (10,1) are collinear

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