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प्रश्न
Determine whether the following point is collinear.
D(–2, –3), E(1, 0), F(2, 1)
उत्तर
D(–2, –3), E(1, 0), F(2, 1)
\[\mathrm{Slope~of~line~DE}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} =\frac{0-\left(-3\right)}{1-\left(-2\right)}\]
= \[\frac{0 + 3}{1 + 2} = \frac{3}{3} = 1\]
\[\mathrm{Slope~of~line~EF}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{1-0}{2-1}=1\]
∴ Slope of DE = Slope of EF = 1
∴ line DE || line EF
Also, point E is common to both the lines.
∴ Both lines are the same.
∴ Points D, E and F are collinear.
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