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)

$$\mathrm{Slope}\mathrm{of}\mathrm{line}\mathrm{DE}=\frac{y_2-y_1}{x_2-x_1}=\frac{0-(-3)}{1-(-2)}$$

= $$\frac{0+3}{1+2}=\frac{3}{3}=1$$

$$\mathrm{Slope}\mathrm{of}\mathrm{line}\mathrm{EF}=\frac{y_2-y_1}{x_2-x_1}=\frac{1-0}{2-1}=1$$

∴ 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.