Question

Determine whether the following point is collinear.

D(–2, –3), E(1, 0), F(2, 1)

Answer 1

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.