The points A(–2, 1), B(0, 5), C(–1, 2) are collinear.

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Vishal Baghel | Contributor-Level 10

8 months ago

This is a True or False Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l} G i v e n a r e A (- 2, 1), B (0, 5), C (- 1, 2) \\ A r e a o f Δ A B C = \frac{1}{2} | \begin{matrix} - 2 & 1 & 1 \\ 0 & 5 & 1 \\ - 1 & 2 & 1 \end{matrix} | \\ = \frac{1}{2} | - 2 | \begin{matrix} 5 & 1 \\ 2 & 1 \end{matrix} | - 1 | \begin{matrix} 0 & 1 \\ - 1 & 1 \end{matrix} | + 1 | \begin{matrix} 0 & 5 \\ - 1 & 2 \end{matrix} | | \\ = \frac{1}{2} | - 2 (5 - 2) - 1 (0 + 1) + 1 (0 + 5) | \\ = \frac{1}{2} | - 2 * 3 - 1 * 1 + 1 * 5 | = \frac{1}{2} | - 6 - 1 + 5 | = \frac{1}{2} | - 2 | = 1 s q . u n i t \\ S o, t h e g i v e n a r e n o t c o l l i n e a r . \\ S o, t h e g i v e n s t a t e m e n t i s F a l s e . \end{array}$

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